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Platonic solid

Index Platonic solid

In three-dimensional space, a Platonic solid is a regular, convex polyhedron. [1]

190 relations: Aether (classical element), Air (classical element), Algebraic surface, Alternation (geometry), Ancient Greece, Ancient Greek philosophy, Andreas Speiser, Angle, Angular defect, Antiprism, Archimedean solid, Aristotle, Astronomer, Brady Haran, Cartesian coordinate system, Carved Stone Balls, Catalan solid, Circumscribed sphere, Classical element, Climatology, Combination puzzle, Combinatorics, Compound of five cubes, Compound of two icosahedra, Congruence (geometry), Convex set, Coxeter element, Coxeter notation, Cross-polytope, Crystal structure, Cubane, Cube, Cuboctahedron, Dan Shechtman, Deltahedron, Dice, Dice notation, Dihedral angle, Dihedron, Dodecahedrane, Dodecahedron, Dual polyhedron, Earth, Earth (classical element), Edge (geometry), Electron configuration, Epinomis, Ernst Haeckel, Euclid, Euclid's Elements, ..., Euclidean group, Euclidean space, Euler characteristic, Face (geometry), Fire (classical element), Genome, Geodesic grid, Goldberg polyhedron, Golden ratio, Group (mathematics), Group action, Hagen Kleinert, Heptagonal tiling, Herpes simplex, Hexagon, Hexagonal tiling, Hosohedron, Hyperbolic geometry, Hypercube, Icosahedral symmetry, Icosahedron, Icosidodecahedron, Inscribed sphere, Isogonal figure, Isohedral figure, Isotoxal figure, Johannes Kepler, Johnson solid, Jupiter, Kepler's laws of planetary motion, Kepler–Poinsot polyhedron, Latitude, Liquid crystal, List of geometers, List of Martin Gardner Mathematical Games columns, List of regular polytopes and compounds, Longitude, Ludwig Schläfli, Lune (geometry), Mars, Martin Gardner, Mercury (planet), Meteorology, Midsphere, Mysterium Cosmographicum, Neolithic, Nobel Prize in Chemistry, Octahedral symmetry, Octahedron, Orbifold notation, Order (group theory), Order-4 pentagonal tiling, Order-5 square tiling, Order-7 triangular tiling, Paul Sutcliffe, Pentagon, Planet, Plato, Platonic hydrocarbon, Point groups in three dimensions, Point reflection, Polygon, Polyhedral combinatorics, Polyhedral group, Polyhedron, Polytope, Polytope compound, Prism (geometry), Proclus, Protein, Pyramid (geometry), Pyrite, Pythagoras, Radiolaria, Radius, Rectification (geometry), Reflection (mathematics), Regular 4-polytope, Regular dodecahedron, Regular icosahedron, Regular polygon, Regular polyhedron, Regular polytope, Regular Polytopes (book), Regular skew polyhedron, Robert James Moon, Role-playing game, Rotation (mathematics), Rubik's Cube, Saturn, Schläfli symbol, Schoenflies notation, Scotland, Simplex, Singularity (mathematics), Solar System, Solid angle, Space frame, Sphere, Spherical trigonometry, Square, Square tiling, Star polygon, Stella (software), Stellated octahedron, Stellation, Steradian, Surface area, Symmetry, Symmetry group, Tessellation, Tesseract, Tetrahedral symmetry, Tetrahedrane, Tetrahedron, Theaetetus (mathematician), Three-dimensional space, Timaeus (dialogue), Topology, Toroidal polyhedron, Triangle, Triangular tiling, Triangulation, Trigonometric functions, Truncated octahedron, Uniform polyhedron, Venus, Vertex (geometry), Vertex configuration, Vertex figure, Virus, Volume, Water (classical element), Wythoff construction, Wythoff symbol, 120-cell, 16-cell, 24-cell, 5-cell, 600-cell. Expand index (140 more) »

Aether (classical element)

According to ancient and medieval science, aether (αἰθήρ aithēr), also spelled æther or ether and also called quintessence, is the material that fills the region of the universe above the terrestrial sphere.

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Air (classical element)

Air is one of the four classical elements in ancient Greek philosophy and in Western alchemy.

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Algebraic surface

In mathematics, an algebraic surface is an algebraic variety of dimension two.

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Alternation (geometry)

In geometry, an alternation or partial truncation, is an operation on a polygon, polyhedron, tiling, or higher dimensional polytope that removes alternate vertices.

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Ancient Greece

Ancient Greece was a civilization belonging to a period of Greek history from the Greek Dark Ages of the 13th–9th centuries BC to the end of antiquity (AD 600).

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Ancient Greek philosophy

Ancient Greek philosophy arose in the 6th century BC and continued throughout the Hellenistic period and the period in which Ancient Greece was part of the Roman Empire.

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Andreas Speiser

Andreas Speiser (June 10, 1885 – October 12, 1970) was a Swiss Mathematician and Philosopher of science.

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Angle

In plane geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

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Angular defect

In geometry, the (angular) defect (or deficit or deficiency) means the failure of some angles to add up to the expected amount of 360° or 180°, when such angles in the Euclidean plane would.

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Antiprism

In geometry, an n-sided antiprism is a polyhedron composed of two parallel copies of some particular n-sided polygon, connected by an alternating band of triangles.

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Archimedean solid

In geometry, an Archimedean solid is one of the 13 solids first enumerated by Archimedes.

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Aristotle

Aristotle (Ἀριστοτέλης Aristotélēs,; 384–322 BC) was an ancient Greek philosopher and scientist born in the city of Stagira, Chalkidiki, in the north of Classical Greece.

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Astronomer

An astronomer is a scientist in the field of astronomy who concentrates their studies on a specific question or field outside the scope of Earth.

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Brady Haran

Brady John Haran (born 18 June 1976) is an Australian-born British independent filmmaker and video journalist who is known for his educational videos and documentary films produced for BBC News and his YouTube channels, the most notable being Periodic Videos and Numberphile.

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Cartesian coordinate system

A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.

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Carved Stone Balls

Carved Stone Balls are petrospheres, usually round and rarely oval.

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Catalan solid

In mathematics, a Catalan solid, or Archimedean dual, is a dual polyhedron to an Archimedean solid.

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Circumscribed sphere

In geometry, a circumscribed sphere of a polyhedron is a sphere that contains the polyhedron and touches each of the polyhedron's vertices.

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Classical element

Classical elements typically refer to the concepts in ancient Greece of earth, water, air, fire, and aether, which were proposed to explain the nature and complexity of all matter in terms of simpler substances.

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Climatology

Climatology (from Greek κλίμα, klima, "place, zone"; and -λογία, -logia) or climate science is the scientific study of climate, scientifically defined as weather conditions averaged over a period of time.

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Combination puzzle

A combination puzzle, also known as a sequential move puzzle, is a puzzle which consists of a set of pieces which can be manipulated into different combinations by a group of operations.

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Combinatorics

Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures.

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Compound of five cubes

The compound of five cubes is one of the five regular polyhedral compounds.

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Compound of two icosahedra

This uniform polyhedron compound is a composition of 2 icosahedra.

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Congruence (geometry)

In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

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Convex set

In convex geometry, a convex set is a subset of an affine space that is closed under convex combinations.

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Coxeter element

In mathematics, the Coxeter number h is the order of a Coxeter element of an irreducible Coxeter group.

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Coxeter notation

In geometry, Coxeter notation (also Coxeter symbol) is a system of classifying symmetry groups, describing the angles between with fundamental reflections of a Coxeter group in a bracketed notation expressing the structure of a Coxeter-Dynkin diagram, with modifiers to indicate certain subgroups.

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Cross-polytope

In geometry, a cross-polytope, orthoplex, hyperoctahedron, or cocube is a regular, convex polytope that exists in n-dimensions.

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Crystal structure

In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions or molecules in a crystalline material.

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Cubane

Cubane (C8H8) is a synthetic hydrocarbon molecule that consists of eight carbon atoms arranged at the corners of a cube, with one hydrogen atom attached to each carbon atom.

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Cube

In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.

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Cuboctahedron

In geometry, a cuboctahedron is a polyhedron with 8 triangular faces and 6 square faces.

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Dan Shechtman

Dan Shechtman (Hebrew: דן שכטמן; born January 24, 1941).

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Deltahedron

In geometry, a deltahedron (plural deltahedra) is a polyhedron whose faces are all equilateral triangles.

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Dice

Dice (singular die or dice; from Old French dé; from Latin datum "something which is given or played") are small throwable objects with multiple resting positions, used for generating random numbers.

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Dice notation

Dice notation (also known as dice algebra, common dice notation, RPG dice notation, and several other titles) is a system to represent different combinations of dice in role-playing games using simple algebra-like notation such as 2d6+12.

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Dihedral angle

A dihedral angle is the angle between two intersecting planes.

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Dihedron

A dihedron is a type of polyhedron, made of two polygon faces which share the same set of edges.

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Dodecahedrane

Dodecahedrane is a chemical compound (C20H20) first synthesised by Leo Paquette of Ohio State University in 1982, primarily for the "aesthetically pleasing symmetry of the dodecahedral framework".

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Dodecahedron

In geometry, a dodecahedron (Greek δωδεκάεδρον, from δώδεκα dōdeka "twelve" + ἕδρα hédra "base", "seat" or "face") is any polyhedron with twelve flat faces.

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Dual polyhedron

In geometry, any polyhedron is associated with a second dual figure, where the vertices of one correspond to the faces of the other and the edges between pairs of vertices of one correspond to the edges between pairs of faces of the other.

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Earth

Earth is the third planet from the Sun and the only astronomical object known to harbor life.

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Earth (classical element)

Earth is one of the classical elements, in some systems numbering four along with air, fire, and water.

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Edge (geometry)

In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope.

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Electron configuration

In atomic physics and quantum chemistry, the electron configuration is the distribution of electrons of an atom or molecule (or other physical structure) in atomic or molecular orbitals.

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Epinomis

The Epinomis (Greek: Ἐπινομίς) is a dialogue attributed to Plato.

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Ernst Haeckel

Ernst Heinrich Philipp August Haeckel (16 February 1834 – 9 August 1919) was a German biologist, naturalist, philosopher, physician, professor, marine biologist, and artist who discovered, described and named thousands of new species, mapped a genealogical tree relating all life forms, and coined many terms in biology, including anthropogeny, ecology, phylum, phylogeny, and Protista. Haeckel promoted and popularised Charles Darwin's work in Germany and developed the influential but no longer widely held recapitulation theory ("ontogeny recapitulates phylogeny") claiming that an individual organism's biological development, or ontogeny, parallels and summarises its species' evolutionary development, or phylogeny.

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Euclid

Euclid (Εὐκλείδης Eukleidēs; fl. 300 BC), sometimes given the name Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry".

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Euclid's Elements

The Elements (Στοιχεῖα Stoicheia) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC.

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Euclidean group

In mathematics, the Euclidean group E(n), also known as ISO(n) or similar, is the symmetry group of n-dimensional Euclidean space.

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Euclidean space

In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.

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Euler characteristic

In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space's shape or structure regardless of the way it is bent.

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Face (geometry)

In solid geometry, a face is a flat (planar) surface that forms part of the boundary of a solid object; a three-dimensional solid bounded exclusively by flat faces is a polyhedron.

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Fire (classical element)

Fire has been an important part of all cultures and religions from pre-history to modern day and was vital to the development of civilization.

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Genome

In the fields of molecular biology and genetics, a genome is the genetic material of an organism.

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Geodesic grid

A geodesic grid is a spatial grid based on a geodesic polyhedron or Goldberg polyhedron.

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Goldberg polyhedron

A Goldberg polyhedron is a convex polyhedron made from hexagons and pentagons.

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Golden ratio

In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.

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Group (mathematics)

In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.

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Group action

In mathematics, an action of a group is a formal way of interpreting the manner in which the elements of the group correspond to transformations of some space in a way that preserves the structure of that space.

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Hagen Kleinert

Hagen Kleinert (born 15 June 1941) is Professor of Theoretical Physics at the Free University of Berlin, Germany (since 1968), at the West University of Timişoara, at the in Bishkek.

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Heptagonal tiling

In geometry, the heptagonal tiling is a regular tiling of the hyperbolic plane.

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Herpes simplex

Herpes simplex is a viral disease caused by the herpes simplex virus.

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Hexagon

In geometry, a hexagon (from Greek ἕξ hex, "six" and γωνία, gonía, "corner, angle") is a six-sided polygon or 6-gon.

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Hexagonal tiling

In geometry, the hexagonal tiling or hexagonal tessellation is a regular tiling of the Euclidean plane, in which three hexagons meet at each vertex.

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Hosohedron

In geometry, an ''n''-gonal hosohedron is a tessellation of lunes on a spherical surface, such that each lune shares the same two polar opposite vertices.

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Hyperbolic geometry

In mathematics, hyperbolic geometry (also called Bolyai–Lobachevskian geometry or Lobachevskian geometry) is a non-Euclidean geometry.

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Hypercube

In geometry, a hypercube is an ''n''-dimensional analogue of a square and a cube.

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Icosahedral symmetry

A regular icosahedron has 60 rotational (or orientation-preserving) symmetries, and a symmetry order of 120 including transformations that combine a reflection and a rotation.

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Icosahedron

In geometry, an icosahedron is a polyhedron with 20 faces.

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Icosidodecahedron

In geometry, an icosidodecahedron is a polyhedron with twenty (icosi) triangular faces and twelve (dodeca) pentagonal faces.

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Inscribed sphere

In geometry, the inscribed sphere or insphere of a convex polyhedron is a sphere that is contained within the polyhedron and tangent to each of the polyhedron's faces.

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Isogonal figure

In geometry, a polytope (a polygon, polyhedron or tiling, for example) is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure.

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Isohedral figure

In geometry, a polytope of dimension 3 (a polyhedron) or higher is isohedral or face-transitive when all its faces are the same.

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Isotoxal figure

In geometry, a polytope (for example, a polygon or a polyhedron), or a tiling, is isotoxal or edge-transitive if its symmetries act transitively on its edges.

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Johannes Kepler

Johannes Kepler (December 27, 1571 – November 15, 1630) was a German mathematician, astronomer, and astrologer.

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Johnson solid

In geometry, a Johnson solid is a strictly convex polyhedron, which is not uniform (i.e., not a Platonic solid, Archimedean solid, prism, or antiprism), and each face of which is a regular polygon.

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Jupiter

Jupiter is the fifth planet from the Sun and the largest in the Solar System.

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Kepler's laws of planetary motion

In astronomy, Kepler's laws of planetary motion are three scientific laws describing the motion of planets around the Sun.

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Kepler–Poinsot polyhedron

In geometry, a Kepler–Poinsot polyhedron is any of four regular star polyhedra.

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Latitude

In geography, latitude is a geographic coordinate that specifies the north–south position of a point on the Earth's surface.

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Liquid crystal

Liquid crystals (LCs) are matter in a state which has properties between those of conventional liquids and those of solid crystals.

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List of geometers

A geometer is a mathematician whose area of study is geometry.

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List of Martin Gardner Mathematical Games columns

Over a period of 24 years (January 1957 – December 1980), Martin Gardner wrote 288 consecutive "Mathematical Games" columns for Scientific American magazine.

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List of regular polytopes and compounds

This page lists the regular polytopes and regular polytope compounds in Euclidean, spherical and hyperbolic spaces.

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Longitude

Longitude, is a geographic coordinate that specifies the east-west position of a point on the Earth's surface.

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Ludwig Schläfli

Ludwig Schläfli (15 January 1814 – 20 March 1895) was a Swiss mathematician, specialising in geometry and complex analysis (at the time called function theory) who was one of the key figures in developing the notion of higher-dimensional spaces.

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Lune (geometry)

In plane geometry, a lune is the concave-convex area bounded by two circular arcs, while a convex-convex area is termed a lens.

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Mars

Mars is the fourth planet from the Sun and the second-smallest planet in the Solar System after Mercury.

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Martin Gardner

Martin Gardner (October 21, 1914May 22, 2010) was an American popular mathematics and popular science writer, with interests also encompassing scientific skepticism, micromagic, philosophy, religion, and literature—especially the writings of Lewis Carroll, L. Frank Baum, and G. K. Chesterton.

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Mercury (planet)

Mercury is the smallest and innermost planet in the Solar System.

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Meteorology

Meteorology is a branch of the atmospheric sciences which includes atmospheric chemistry and atmospheric physics, with a major focus on weather forecasting.

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Midsphere

In geometry, the midsphere or intersphere of a polyhedron is a sphere which is tangent to every edge of the polyhedron.

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Mysterium Cosmographicum

Mysterium Cosmographicum (lit. The Cosmographic Mystery, alternately translated as Cosmic Mystery, The Secret of the World, or some variation) is an astronomy book by the German astronomer Johannes Kepler, published at Tübingen in 1596 and in a second edition in 1621.

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Neolithic

The Neolithic was a period in the development of human technology, beginning about 10,200 BC, according to the ASPRO chronology, in some parts of Western Asia, and later in other parts of the world and ending between 4500 and 2000 BC.

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Nobel Prize in Chemistry

The Nobel Prize in Chemistry (Nobelpriset i kemi) is awarded annually by the Royal Swedish Academy of Sciences to scientists in the various fields of chemistry.

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Octahedral symmetry

A regular octahedron has 24 rotational (or orientation-preserving) symmetries, and a symmetry order of 48 including transformations that combine a reflection and a rotation.

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Octahedron

In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces, twelve edges, and six vertices.

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Orbifold notation

In geometry, orbifold notation (or orbifold signature) is a system, invented by William Thurston and popularized by the mathematician John Conway, for representing types of symmetry groups in two-dimensional spaces of constant curvature.

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Order (group theory)

In group theory, a branch of mathematics, the term order is used in two unrelated senses.

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Order-4 pentagonal tiling

In geometry, the order-4 pentagonal tiling is a regular tiling of the hyperbolic plane.

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Order-5 square tiling

In geometry, the order-5 square tiling is a regular tiling of the hyperbolic plane.

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Order-7 triangular tiling

In geometry, the order-7 triangular tiling is a regular tiling of the hyperbolic plane with a Schläfli symbol of.

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Paul Sutcliffe

Paul Sutcliffe is British mathematical physicist and mathematician, currently Professor of Theoretical Physics at the University of Durham.

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Pentagon

In geometry, a pentagon (from the Greek πέντε pente and γωνία gonia, meaning five and angle) is any five-sided polygon or 5-gon.

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Planet

A planet is an astronomical body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared its neighbouring region of planetesimals.

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Plato

Plato (Πλάτων Plátōn, in Classical Attic; 428/427 or 424/423 – 348/347 BC) was a philosopher in Classical Greece and the founder of the Academy in Athens, the first institution of higher learning in the Western world.

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Platonic hydrocarbon

A Platonic hydrocarbon is a hydrocarbon (molecule) whose structure matches one of the five Platonic solids, with carbon atoms replacing its vertices, carbon–carbon bonds replacing its edges, and hydrogen atoms as needed.

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Point groups in three dimensions

In geometry, a point group in three dimensions is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, an isometry group of a sphere.

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Point reflection

In geometry, a point reflection or inversion in a point (or inversion through a point, or central inversion) is a type of isometry of Euclidean space.

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Polygon

In elementary geometry, a polygon is a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed polygonal chain or circuit.

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Polyhedral combinatorics

Polyhedral combinatorics is a branch of mathematics, within combinatorics and discrete geometry, that studies the problems of counting and describing the faces of convex polyhedra and higher-dimensional convex polytopes.

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Polyhedral group

In geometry, the polyhedral group is any of the symmetry groups of the Platonic solids.

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Polyhedron

In geometry, a polyhedron (plural polyhedra or polyhedrons) is a solid in three dimensions with flat polygonal faces, straight edges and sharp corners or vertices.

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Polytope

In elementary geometry, a polytope is a geometric object with "flat" sides.

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Polytope compound

A polyhedral compound is a figure that is composed of several polyhedra sharing a common centre.

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Prism (geometry)

In geometry, a prism is a polyhedron comprising an n-sided polygonal base, a second base which is a translated copy (rigidly moved without rotation) of the first, and n other faces (necessarily all parallelograms) joining corresponding sides of the two bases.

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Proclus

Proclus Lycaeus (8 February 412 – 17 April 485 AD), called the Successor (Greek Πρόκλος ὁ Διάδοχος, Próklos ho Diádokhos), was a Greek Neoplatonist philosopher, one of the last major classical philosophers (see Damascius).

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Protein

Proteins are large biomolecules, or macromolecules, consisting of one or more long chains of amino acid residues.

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Pyramid (geometry)

In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex.

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Pyrite

The mineral pyrite, or iron pyrite, also known as fool's gold, is an iron sulfide with the chemical formula FeS2 (iron(II) disulfide).

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Pythagoras

Pythagoras of Samos was an Ionian Greek philosopher and the eponymous founder of the Pythagoreanism movement.

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Radiolaria

The Radiolaria, also called Radiozoa, are protozoa of diameter 0.1–0.2 mm that produce intricate mineral skeletons, typically with a central capsule dividing the cell into the inner and outer portions of endoplasm and ectoplasm.The elaborate mineral skeleton is usually made of silica.

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Radius

In classical geometry, a radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length.

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Rectification (geometry)

In Euclidean geometry, rectification or complete-truncation is the process of truncating a polytope by marking the midpoints of all its edges, and cutting off its vertices at those points.

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Reflection (mathematics)

In mathematics, a reflection (also spelled reflexion) is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; this set is called the axis (in dimension 2) or plane (in dimension 3) of reflection.

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Regular 4-polytope

In mathematics, a regular 4-polytope is a regular four-dimensional polytope.

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Regular dodecahedron

A regular dodecahedron or pentagonal dodecahedron is a dodecahedron that is regular, which is composed of twelve regular pentagonal faces, three meeting at each vertex.

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Regular icosahedron

In geometry, a regular icosahedron is a convex polyhedron with 20 faces, 30 edges and 12 vertices.

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Regular polygon

In Euclidean geometry, a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).

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Regular polyhedron

A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags.

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Regular polytope

In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry.

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Regular Polytopes (book)

Regular Polytopes is a mathematical geometry book written by Canadian mathematician Harold Scott MacDonald Coxeter.

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Regular skew polyhedron

In geometry, the regular skew polyhedra are generalizations to the set of regular polyhedron which include the possibility of nonplanar faces or vertex figures.

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Robert James Moon

Robert James Moon (February 14, 1911November 1, 1989) was an American physicist, chemist and engineer.

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Role-playing game

A role-playing game (sometimes spelled roleplaying game and abbreviated to RPG) is a game in which players assume the roles of characters in a fictional setting.

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Rotation (mathematics)

Rotation in mathematics is a concept originating in geometry.

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Rubik's Cube

Rubik's Cube is a 3-D combination puzzle invented in 1974 by Hungarian sculptor and professor of architecture Ernő Rubik.

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Saturn

Saturn is the sixth planet from the Sun and the second-largest in the Solar System, after Jupiter.

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Schläfli symbol

In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.

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Schoenflies notation

The Schoenflies (or Schönflies) notation, named after the German mathematician Arthur Moritz Schoenflies, is one of two conventions commonly used to describe point groups.

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Scotland

Scotland (Alba) is a country that is part of the United Kingdom and covers the northern third of the island of Great Britain.

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Simplex

In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions.

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Singularity (mathematics)

In mathematics, a singularity is in general a point at which a given mathematical object is not defined, or a point of an exceptional set where it fails to be well-behaved in some particular way, such as differentiability.

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Solar System

The Solar SystemCapitalization of the name varies.

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Solid angle

In geometry, a solid angle (symbol) is a measure of the amount of the field of view from some particular point that a given object covers.

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Space frame

In architecture and structural engineering, a space frame or space structure is a rigid, lightweight, truss-like structure constructed from interlocking struts in a geometric pattern.

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Sphere

A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk").

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Spherical trigonometry

Spherical trigonometry is the branch of spherical geometry that deals with the relationships between trigonometric functions of the sides and angles of the spherical polygons (especially spherical triangles) defined by a number of intersecting great circles on the sphere.

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Square

In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or (100-gradian angles or right angles). It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted.

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Square tiling

In geometry, the square tiling, square tessellation or square grid is a regular tiling of the Euclidean plane.

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Star polygon

In geometry, a star polygon is a type of non-convex polygon.

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Stella (software)

Stella, a computer program available in three versions (Great Stella, Small Stella and Stella4D), was created by Robert Webb of Australia.

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Stellated octahedron

The stellated octahedron is the only stellation of the octahedron.

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Stellation

In geometry, stellation is the process of extending a polygon in two dimensions, polyhedron in three dimensions, or, in general, a polytope in n dimensions to form a new figure.

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Steradian

No description.

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Surface area

The surface area of a solid object is a measure of the total area that the surface of the object occupies.

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Symmetry

Symmetry (from Greek συμμετρία symmetria "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance.

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Symmetry group

In group theory, the symmetry group of an object (image, signal, etc.) is the group of all transformations under which the object is invariant with composition as the group operation.

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Tessellation

A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps.

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Tesseract

In geometry, the tesseract is the four-dimensional analogue of the cube; the tesseract is to the cube as the cube is to the square.

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Tetrahedral symmetry

A regular tetrahedron, an example of a solid with full tetrahedral symmetry A regular tetrahedron has 12 rotational (or orientation-preserving) symmetries, and a symmetry order of 24 including transformations that combine a reflection and a rotation.

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Tetrahedrane

Tetrahedrane is a platonic hydrocarbon with chemical formula and a tetrahedral structure.

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Tetrahedron

In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners.

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Theaetetus (mathematician)

Theaetetus of Athens (Θεαίτητος; c. 417 – 369 BC), possibly the son of Euphronius of the Athenian deme Sunium, was a Greek mathematician.

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Three-dimensional space

Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameters) are required to determine the position of an element (i.e., point).

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Timaeus (dialogue)

Timaeus (Timaios) is one of Plato's dialogues, mostly in the form of a long monologue given by the title character Timaeus of Locri, written c. 360 BC.

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Topology

In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.

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Toroidal polyhedron

In geometry, a toroidal polyhedron is a polyhedron which is also a toroid (a g-holed torus), having a topological genus of 1 or greater.

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Triangle

A triangle is a polygon with three edges and three vertices.

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Triangular tiling

In geometry, the triangular tiling or triangular tessellation is one of the three regular tilings of the Euclidean plane.

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Triangulation

In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to it from known points.

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Trigonometric functions

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are functions of an angle.

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Truncated octahedron

In geometry, the truncated octahedron is an Archimedean solid.

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Uniform polyhedron

A uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive (transitive on its vertices, isogonal, i.e. there is an isometry mapping any vertex onto any other).

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Venus

Venus is the second planet from the Sun, orbiting it every 224.7 Earth days.

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Vertex (geometry)

In geometry, a vertex (plural: vertices or vertexes) is a point where two or more curves, lines, or edges meet.

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Vertex configuration

In geometry, a vertex configuration by Walter Steurer, Sofia Deloudi, (2009) pp.

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Vertex figure

In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off.

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Virus

A virus is a small infectious agent that replicates only inside the living cells of other organisms.

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Volume

Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains.

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Water (classical element)

Water is one of the elements in ancient Greek philosophy, in the Asian Indian system Panchamahabhuta, and in the Chinese cosmological and physiological system Wu Xing.

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Wythoff construction

In geometry, a Wythoff construction, named after mathematician Willem Abraham Wythoff, is a method for constructing a uniform polyhedron or plane tiling.

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Wythoff symbol

In geometry, the Wythoff symbol represents a Wythoff construction of a uniform polyhedron or plane tiling, from a Schwarz triangle.

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120-cell

In geometry, the 120-cell is the convex regular 4-polytope with Schläfli symbol.

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16-cell

In four-dimensional geometry, a 16-cell is a regular convex 4-polytope.

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24-cell

In geometry, the 24-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol.

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5-cell

In geometry, the 5-cell is a four-dimensional object bounded by 5 tetrahedral cells.

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600-cell

In geometry, the 600-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol.

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References

[1] https://en.wikipedia.org/wiki/Platonic_solid

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