Logo
Unionpedia
Communication
Get it on Google Play
New! Download Unionpedia on your Android™ device!
Install
Faster access than browser!
 

Regular polyhedron

Index Regular polyhedron

A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags. [1]

138 relations: Abstract polytope, Angular defect, Area, Ashmolean Museum, Asymptote, Athens, Carbon, Circumscribed sphere, Complex affine space, Complex polytope, Congruence (geometry), Convex polygon, Coxeter element, Crystal, Cube, Degeneracy (mathematics), Digon, Dihedral angle, Dihedron, Ditrigonal dodecadodecahedron, Dodecadodecahedron, Dodecahedron, Dual polyhedron, Duncan Sommerville, Duocylinder, Duoprism, Elliptic geometry, Ernst Haeckel, Etruscan civilization, Euclidean space, Euler characteristic, Excavated dodecahedron, Facet (geometry), Faceting, Flag (geometry), Fullerene, Great circle, Great dodecahedron, Great icosahedron, Great stellated dodecahedron, Great triambic icosahedron, Harold Scott MacDonald Coxeter, Hemi-dodecahedron, Hemi-icosahedron, Hemi-octahedron, Hemicube (geometry), Hexagon, HIV, Hosohedron, Hyperbolic space, ..., Ideal point, Inscribed sphere, Isogonal figure, Isohedral figure, Isotoxal figure, Italy, Johannes Kepler, John Dalton, Joseph Bertrand, Kepler's laws of planetary motion, Kepler–Poinsot polyhedron, Kunstformen der Natur, Louis Poinsot, Medial rhombic triacontahedron, Midsphere, Neptune, Non-Euclidean geometry, Octagon, Octahedron, Order-4 pentagonal tiling, Order-5 hexagonal tiling, Order-5 square tiling, Order-6 hexagonal tiling, Order-6 pentagonal tiling, Padua, Paracompact uniform honeycombs, Partially ordered set, Pentagon, Pentagram, Petrie dual, Petrie polygon, Planet, Plato, Platonic solid, Polygon, Polyhedral combinatorics, Polyhedron, Polytope, Prism (geometry), Projective polyhedron, Pythagoreanism, Quasicrystal, Quasiregular polyhedron, Radiolaria, Real projective plane, Regular dodecahedron, Regular icosahedron, Regular map (graph theory), Regular polygon, Regular polytope, Regular Polytopes (book), Regular skew polyhedron, Schläfli symbol, Scotland, Semiregular polyhedron, Skew polygon, Small stellated dodecahedron, Soapstone, Solid angle, Sphere, Spherical polyhedron, Square, Square pyramid, Star polyhedron, Stellation, Stereographic projection, Symmetry, Symmetry group, Tetrahedron, The College Mathematics Journal, Theaetetus (mathematician), Timaeus (dialogue), Timaeus of Locri, Toroid, Torus, Triangle, Triangular bipyramid, Tycho Brahe, Uniform 4-polytope, Uniform polyhedron, University of Oxford, Uranus, Vertex (geometry), Vertex figure, Virus, Viviani's theorem, 24-cell, 5-cell. Expand index (88 more) »

Abstract polytope

In mathematics, an abstract polytope is an algebraic partially ordered set or poset which captures the combinatorial properties of a traditional polytope, but not any purely geometric properties such as angles, edge lengths, etc.

New!!: Regular polyhedron and Abstract polytope · See more »

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.

New!!: Regular polyhedron and Angular defect · See more »

Area

Area is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane.

New!!: Regular polyhedron and Area · See more »

Ashmolean Museum

The Ashmolean Museum (in full the Ashmolean Museum of Art and Archaeology) on Beaumont Street, Oxford, England, is the world's first university museum.

New!!: Regular polyhedron and Ashmolean Museum · See more »

Asymptote

In analytic geometry, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the x or y coordinates tends to infinity.

New!!: Regular polyhedron and Asymptote · See more »

Athens

Athens (Αθήνα, Athína; Ἀθῆναι, Athênai) is the capital and largest city of Greece.

New!!: Regular polyhedron and Athens · See more »

Carbon

Carbon (from carbo "coal") is a chemical element with symbol C and atomic number 6.

New!!: Regular polyhedron and Carbon · See more »

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.

New!!: Regular polyhedron and Circumscribed sphere · See more »

Complex affine space

Affine geometry, broadly speaking, is the study of the geometrical properties of lines, planes, and their higher dimensional analogs, in which a notion of "parallel" is retained, but no metrical notions of distance or angle are.

New!!: Regular polyhedron and Complex affine space · See more »

Complex polytope

In geometry, a complex polytope is a generalization of a polytope in real space to an analogous structure in a complex Hilbert space, where each real dimension is accompanied by an imaginary one.

New!!: Regular polyhedron and Complex polytope · See more »

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.

New!!: Regular polyhedron and Congruence (geometry) · See more »

Convex polygon

A convex polygon is a simple polygon (not self-intersecting) in which no line segment between two points on the boundary ever goes outside the polygon.

New!!: Regular polyhedron and Convex polygon · See more »

Coxeter element

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

New!!: Regular polyhedron and Coxeter element · See more »

Crystal

A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions.

New!!: Regular polyhedron and Crystal · See more »

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.

New!!: Regular polyhedron and Cube · See more »

Degeneracy (mathematics)

In mathematics, a degenerate case is a limiting case in which an element of a class of objects is qualitatively different from the rest of the class and hence belongs to another, usually simpler, class.

New!!: Regular polyhedron and Degeneracy (mathematics) · See more »

Digon

In geometry, a digon is a polygon with two sides (edges) and two vertices.

New!!: Regular polyhedron and Digon · See more »

Dihedral angle

A dihedral angle is the angle between two intersecting planes.

New!!: Regular polyhedron and Dihedral angle · See more »

Dihedron

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

New!!: Regular polyhedron and Dihedron · See more »

Ditrigonal dodecadodecahedron

In geometry, the ditrigonal dodecadodecahedron is a nonconvex uniform polyhedron, indexed as U41.

New!!: Regular polyhedron and Ditrigonal dodecadodecahedron · See more »

Dodecadodecahedron

In geometry, the dodecadodecahedron is a nonconvex uniform polyhedron, indexed as U36.

New!!: Regular polyhedron and Dodecadodecahedron · See more »

Dodecahedron

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

New!!: Regular polyhedron and Dodecahedron · See more »

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.

New!!: Regular polyhedron and Dual polyhedron · See more »

Duncan Sommerville

Duncan MacLaren Young Sommerville (1879–1934) was a Scottish mathematician and astronomer.

New!!: Regular polyhedron and Duncan Sommerville · See more »

Duocylinder

The duocylinder, or double cylinder, is a geometric object embedded in 4-dimensional Euclidean space, defined as the Cartesian product of two disks of respective radii r1 and r2: It is analogous to a cylinder in 3-space, which is the Cartesian product of a disk with a line segment.

New!!: Regular polyhedron and Duocylinder · See more »

Duoprism

In geometry of 4 dimensions or higher, a duoprism is a polytope resulting from the Cartesian product of two polytopes, each of two dimensions or higher.

New!!: Regular polyhedron and Duoprism · See more »

Elliptic geometry

Elliptic geometry is a geometry in which Euclid's parallel postulate does not hold.

New!!: Regular polyhedron and Elliptic geometry · See more »

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.

New!!: Regular polyhedron and Ernst Haeckel · See more »

Etruscan civilization

The Etruscan civilization is the modern name given to a powerful and wealthy civilization of ancient Italy in the area corresponding roughly to Tuscany, western Umbria and northern Lazio.

New!!: Regular polyhedron and Etruscan civilization · See more »

Euclidean space

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

New!!: Regular polyhedron and Euclidean space · See more »

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.

New!!: Regular polyhedron and Euler characteristic · See more »

Excavated dodecahedron

In geometry, the excavated dodecahedron is a star polyhedron having 60 equilateral triangular faces.

New!!: Regular polyhedron and Excavated dodecahedron · See more »

Facet (geometry)

In geometry, a facet is a feature of a polyhedron, polytope, or related geometric structure, generally of dimension one less than the structure itself.

New!!: Regular polyhedron and Facet (geometry) · See more »

Faceting

Stella octangula as a faceting of the cube In geometry, faceting (also spelled facetting) is the process of removing parts of a polygon, polyhedron or polytope, without creating any new vertices.

New!!: Regular polyhedron and Faceting · See more »

Flag (geometry)

In (polyhedral) geometry, a flag is a sequence of faces of a polytope, each contained in the next, with exactly one face from each dimension.

New!!: Regular polyhedron and Flag (geometry) · See more »

Fullerene

A fullerene is a molecule of carbon in the form of a hollow sphere, ellipsoid, tube, and many other shapes.

New!!: Regular polyhedron and Fullerene · See more »

Great circle

A great circle, also known as an orthodrome, of a sphere is the intersection of the sphere and a plane that passes through the center point of the sphere.

New!!: Regular polyhedron and Great circle · See more »

Great dodecahedron

In geometry, the great dodecahedron is a Kepler–Poinsot polyhedron, with Schläfli symbol and Coxeter–Dynkin diagram of.

New!!: Regular polyhedron and Great dodecahedron · See more »

Great icosahedron

In geometry, the great icosahedron is one of four Kepler-Poinsot polyhedra (nonconvex regular polyhedra), with Schläfli symbol and Coxeter-Dynkin diagram of.

New!!: Regular polyhedron and Great icosahedron · See more »

Great stellated dodecahedron

In geometry, the great stellated dodecahedron is a Kepler-Poinsot polyhedron, with Schläfli symbol.

New!!: Regular polyhedron and Great stellated dodecahedron · See more »

Great triambic icosahedron

In geometry, the great triambic icosahedron and medial triambic icosahedron are visually identical dual uniform polyhedra.

New!!: Regular polyhedron and Great triambic icosahedron · See more »

Harold Scott MacDonald Coxeter

Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 – March 31, 2003) was a British-born Canadian geometer.

New!!: Regular polyhedron and Harold Scott MacDonald Coxeter · See more »

Hemi-dodecahedron

A hemi-dodecahedron is an abstract regular polyhedron, containing half the faces of a regular dodecahedron.

New!!: Regular polyhedron and Hemi-dodecahedron · See more »

Hemi-icosahedron

A hemi-icosahedron is an abstract regular polyhedron, containing half the faces of a regular icosahedron.

New!!: Regular polyhedron and Hemi-icosahedron · See more »

Hemi-octahedron

A hemi-octahedron is an abstract regular polyhedron, containing half the faces of a regular octahedron.

New!!: Regular polyhedron and Hemi-octahedron · See more »

Hemicube (geometry)

In abstract geometry, a hemicube is an abstract regular polyhedron, containing half the faces of a cube.

New!!: Regular polyhedron and Hemicube (geometry) · See more »

Hexagon

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

New!!: Regular polyhedron and Hexagon · See more »

HIV

The human immunodeficiency virus (HIV) is a lentivirus (a subgroup of retrovirus) that causes HIV infection and over time acquired immunodeficiency syndrome (AIDS).

New!!: Regular polyhedron and HIV · See more »

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.

New!!: Regular polyhedron and Hosohedron · See more »

Hyperbolic space

In mathematics, hyperbolic space is a homogeneous space that has a constant negative curvature, where in this case the curvature is the sectional curvature.

New!!: Regular polyhedron and Hyperbolic space · See more »

Ideal point

In hyperbolic geometry, an ideal point, omega point or point at infinity is a well defined point outside the hyperbolic plane or space.

New!!: Regular polyhedron and Ideal point · See more »

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.

New!!: Regular polyhedron and Inscribed sphere · See more »

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.

New!!: Regular polyhedron and Isogonal figure · See more »

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.

New!!: Regular polyhedron and Isohedral figure · See more »

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.

New!!: Regular polyhedron and Isotoxal figure · See more »

Italy

Italy (Italia), officially the Italian Republic (Repubblica Italiana), is a sovereign state in Europe.

New!!: Regular polyhedron and Italy · See more »

Johannes Kepler

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

New!!: Regular polyhedron and Johannes Kepler · See more »

John Dalton

John Dalton FRS (6 September 1766 – 27 July 1844) was an English chemist, physicist, and meteorologist.

New!!: Regular polyhedron and John Dalton · See more »

Joseph Bertrand

Joseph Louis François Bertrand (11 March 1822 – 5 April 1900) was a French mathematician who worked in the fields of number theory, differential geometry, probability theory, economics and thermodynamics.

New!!: Regular polyhedron and Joseph Bertrand · See more »

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.

New!!: Regular polyhedron and Kepler's laws of planetary motion · See more »

Kepler–Poinsot polyhedron

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

New!!: Regular polyhedron and Kepler–Poinsot polyhedron · See more »

Kunstformen der Natur

Kunstformen der Natur (known in English as Art Forms in Nature) is a book of lithographic and halftone prints by German biologist Ernst Haeckel.

New!!: Regular polyhedron and Kunstformen der Natur · See more »

Louis Poinsot

Louis Poinsot (3 January 1777 – 5 December 1859) was a French mathematician and physicist.

New!!: Regular polyhedron and Louis Poinsot · See more »

Medial rhombic triacontahedron

In geometry, the medial rhombic triacontahedron is a nonconvex isohedral polyhedron.

New!!: Regular polyhedron and Medial rhombic triacontahedron · See more »

Midsphere

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

New!!: Regular polyhedron and Midsphere · See more »

Neptune

Neptune is the eighth and farthest known planet from the Sun in the Solar System.

New!!: Regular polyhedron and Neptune · See more »

Non-Euclidean geometry

In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those specifying Euclidean geometry.

New!!: Regular polyhedron and Non-Euclidean geometry · See more »

Octagon

In geometry, an octagon (from the Greek ὀκτάγωνον oktágōnon, "eight angles") is an eight-sided polygon or 8-gon.

New!!: Regular polyhedron and Octagon · See more »

Octahedron

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

New!!: Regular polyhedron and Octahedron · See more »

Order-4 pentagonal tiling

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

New!!: Regular polyhedron and Order-4 pentagonal tiling · See more »

Order-5 hexagonal tiling

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

New!!: Regular polyhedron and Order-5 hexagonal tiling · See more »

Order-5 square tiling

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

New!!: Regular polyhedron and Order-5 square tiling · See more »

Order-6 hexagonal tiling

In geometry, the order-6 hexagonal tiling is a regular tiling of the hyperbolic plane.

New!!: Regular polyhedron and Order-6 hexagonal tiling · See more »

Order-6 pentagonal tiling

In geometry, the order-6 pentagonal tiling is a regular tiling of the hyperbolic plane.

New!!: Regular polyhedron and Order-6 pentagonal tiling · See more »

Padua

Padua (Padova; Pàdova) is a city and comune in Veneto, northern Italy.

New!!: Regular polyhedron and Padua · See more »

Paracompact uniform honeycombs

In geometry, uniform honeycombs in hyperbolic space are tessellations of convex uniform polyhedron cells.

New!!: Regular polyhedron and Paracompact uniform honeycombs · See more »

Partially ordered set

In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set.

New!!: Regular polyhedron and Partially ordered set · See more »

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.

New!!: Regular polyhedron and Pentagon · See more »

Pentagram

A pentagram (sometimes known as a pentalpha or pentangle or a star pentagon) is the shape of a five-pointed star drawn with five straight strokes.

New!!: Regular polyhedron and Pentagram · See more »

Petrie dual

In topological graph theory, the Petrie dual of a embedded graph (on a 2-manifold with all faces disks) is another embedded graph that has the Petrie polygons of the first embedding as its faces.

New!!: Regular polyhedron and Petrie dual · See more »

Petrie polygon

In geometry, a Petrie polygon for a regular polytope of n dimensions is a skew polygon in which every (n – 1) consecutive sides (but no n) belongs to one of the facets.

New!!: Regular polyhedron and Petrie polygon · See more »

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.

New!!: Regular polyhedron and Planet · See more »

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.

New!!: Regular polyhedron and Plato · See more »

Platonic solid

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

New!!: Regular polyhedron and Platonic solid · See more »

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.

New!!: Regular polyhedron and Polygon · See more »

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.

New!!: Regular polyhedron and Polyhedral combinatorics · See more »

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.

New!!: Regular polyhedron and Polyhedron · See more »

Polytope

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

New!!: Regular polyhedron and Polytope · See more »

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.

New!!: Regular polyhedron and Prism (geometry) · See more »

Projective polyhedron

In geometry, a (globally) projective polyhedron is a tessellation of the real projective plane.

New!!: Regular polyhedron and Projective polyhedron · See more »

Pythagoreanism

Pythagoreanism originated in the 6th century BC, based on the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans, who were considerably influenced by mathematics and mysticism.

New!!: Regular polyhedron and Pythagoreanism · See more »

Quasicrystal

A quasiperiodic crystal, or quasicrystal, is a structure that is ordered but not periodic.

New!!: Regular polyhedron and Quasicrystal · See more »

Quasiregular polyhedron

In geometry, a quasiregular polyhedron is a semiregular polyhedron that has exactly two kinds of regular faces, which alternate around each vertex.

New!!: Regular polyhedron and Quasiregular polyhedron · See more »

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.

New!!: Regular polyhedron and Radiolaria · See more »

Real projective plane

In mathematics, the real projective plane is an example of a compact non-orientable two-dimensional manifold; in other words, a one-sided surface.

New!!: Regular polyhedron and Real projective plane · See more »

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.

New!!: Regular polyhedron and Regular dodecahedron · See more »

Regular icosahedron

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

New!!: Regular polyhedron and Regular icosahedron · See more »

Regular map (graph theory)

In mathematics, a regular map is a symmetric tessellation of a closed surface.

New!!: Regular polyhedron and Regular map (graph theory) · See more »

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).

New!!: Regular polyhedron and Regular polygon · See more »

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.

New!!: Regular polyhedron and Regular polytope · See more »

Regular Polytopes (book)

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

New!!: Regular polyhedron and Regular Polytopes (book) · See more »

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.

New!!: Regular polyhedron and Regular skew polyhedron · See more »

Schläfli symbol

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

New!!: Regular polyhedron and Schläfli symbol · See more »

Scotland

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

New!!: Regular polyhedron and Scotland · See more »

Semiregular polyhedron

The term semiregular polyhedron (or semiregular polytope) is used variously by different authors.

New!!: Regular polyhedron and Semiregular polyhedron · See more »

Skew polygon

In geometry, a skew polygon is a polygon whose vertices are not all coplanar.

New!!: Regular polyhedron and Skew polygon · See more »

Small stellated dodecahedron

In geometry, the small stellated dodecahedron is a Kepler-Poinsot polyhedron, named by Arthur Cayley, and with Schläfli symbol.

New!!: Regular polyhedron and Small stellated dodecahedron · See more »

Soapstone

Soapstone (also known as steatite or soaprock) is a talc-schist, which is a type of metamorphic rock.

New!!: Regular polyhedron and Soapstone · See more »

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.

New!!: Regular polyhedron and Solid angle · See more »

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").

New!!: Regular polyhedron and Sphere · See more »

Spherical polyhedron

In mathematics, a spherical polyhedron or spherical tiling is a tiling of the sphere in which the surface is divided or partitioned by great arcs into bounded regions called spherical polygons.

New!!: Regular polyhedron and Spherical polyhedron · See more »

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.

New!!: Regular polyhedron and Square · See more »

Square pyramid

In geometry, a square pyramid is a pyramid having a square base.

New!!: Regular polyhedron and Square pyramid · See more »

Star polyhedron

In geometry, a star polyhedron is a polyhedron which has some repetitive quality of nonconvexity giving it a star-like visual quality.

New!!: Regular polyhedron and Star polyhedron · See more »

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.

New!!: Regular polyhedron and Stellation · See more »

Stereographic projection

In geometry, the stereographic projection is a particular mapping (function) that projects a sphere onto a plane.

New!!: Regular polyhedron and Stereographic projection · See more »

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.

New!!: Regular polyhedron and Symmetry · See more »

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.

New!!: Regular polyhedron and Symmetry group · See more »

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.

New!!: Regular polyhedron and Tetrahedron · See more »

The College Mathematics Journal

The College Mathematics Journal, published by the Mathematical Association of America, is an expository journal aimed at teachers of college mathematics, particular those teaching the first two years.

New!!: Regular polyhedron and The College Mathematics Journal · See more »

Theaetetus (mathematician)

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

New!!: Regular polyhedron and Theaetetus (mathematician) · See more »

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.

New!!: Regular polyhedron and Timaeus (dialogue) · See more »

Timaeus of Locri

Timaeus of Locri (Tímaios ho Lokrós; Timaeus Locrus) is a character in two of Plato's dialogues, Timaeus and Critias.

New!!: Regular polyhedron and Timaeus of Locri · See more »

Toroid

In mathematics, a toroid is a surface of revolution with a hole in the middle, like a doughnut, forming a solid body.

New!!: Regular polyhedron and Toroid · See more »

Torus

In geometry, a torus (plural tori) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle.

New!!: Regular polyhedron and Torus · See more »

Triangle

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

New!!: Regular polyhedron and Triangle · See more »

Triangular bipyramid

In geometry, the triangular bipyramid (or dipyramid) is a type of hexahedron, being the first in the infinite set of face-transitive bipyramids.

New!!: Regular polyhedron and Triangular bipyramid · See more »

Tycho Brahe

Tycho Brahe (born Tyge Ottesen Brahe;. He adopted the Latinized form "Tycho Brahe" (sometimes written Tÿcho) at around age fifteen. The name Tycho comes from Tyche (Τύχη, meaning "luck" in Greek, Roman equivalent: Fortuna), a tutelary deity of fortune and prosperity of ancient Greek city cults. He is now generally referred to as "Tycho," as was common in Scandinavia in his time, rather than by his surname "Brahe" (a spurious appellative form of his name, Tycho de Brahe, only appears much later). 14 December 154624 October 1601) was a Danish nobleman, astronomer, and writer known for his accurate and comprehensive astronomical and planetary observations.

New!!: Regular polyhedron and Tycho Brahe · See more »

Uniform 4-polytope

In geometry, a uniform 4-polytope (or uniform polychoron) is a 4-polytope which is vertex-transitive and whose cells are uniform polyhedra, and faces are regular polygons.

New!!: Regular polyhedron and Uniform 4-polytope · See more »

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).

New!!: Regular polyhedron and Uniform polyhedron · See more »

University of Oxford

The University of Oxford (formally The Chancellor Masters and Scholars of the University of Oxford) is a collegiate research university located in Oxford, England.

New!!: Regular polyhedron and University of Oxford · See more »

Uranus

Uranus is the seventh planet from the Sun.

New!!: Regular polyhedron and Uranus · See more »

Vertex (geometry)

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

New!!: Regular polyhedron and Vertex (geometry) · See more »

Vertex figure

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

New!!: Regular polyhedron and Vertex figure · See more »

Virus

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

New!!: Regular polyhedron and Virus · See more »

Viviani's theorem

Viviani's theorem, named after Vincenzo Viviani, states that the sum of the distances from any interior point to the sides of an equilateral triangle equals the length of the triangle's altitude.

New!!: Regular polyhedron and Viviani's theorem · See more »

24-cell

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

New!!: Regular polyhedron and 24-cell · See more »

5-cell

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

New!!: Regular polyhedron and 5-cell · See more »

Redirects here:

Petrial cube, Petrial dodecahedron, Petrial icosahedron, Petrial octahedron, Petrial tetrahedron, Petrie cube, Regular 3-polytope, Regular polyhedra.

References

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

OutgoingIncoming
Hey! We are on Facebook now! »