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Regular dodecahedron

Index 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. [1]

114 relations: Aether (classical element), Alternating group, Apothem, Aristotle, Avant-garde metal, Bertrand Russell, Bilunabirotunda, Cartesian coordinate system, Circumscribed sphere, Classical element, Compound of five cubes, Compound of five tetrahedra, Compound of ten tetrahedra, Coxeter element, Coxeter group, Crystal habit, Cube, Cyclic group, Diamond, Dihedral angle, Direct product of groups, Distance (graph theory), Distance-regular graph, Distance-transitive graph, Ditrigonal dodecadodecahedron, Dodecahedrane, Dodecahedron, Dual polyhedron, Face diagonal, Florian Cajori, Garnet, Generalized Petersen graph, Gerard Caris, Golden ratio, Graph (discrete mathematics), Graph automorphism, Graph coloring, Gravitation (M. C. Escher), Great ditrigonal icosidodecahedron, Great dodecahedron, Great stellated dodecahedron, Hamiltonian path, Hellenistic period, Iamblichus, Icosahedral symmetry, Icosian game, Icosidodecahedron, Immersive Media, Inverse trigonometric functions, Isohedral figure, ..., Jean-Pierre Luminet, Johnson solid, K-vertex-connected graph, Kepler–Poinsot polyhedron, M. C. Escher, Mathematical game, Megaminx, N-skeleton, Net (polyhedron), Orbifold notation, Orthographic projection, Pentagon, Pentagonal trapezohedron, Pentakis dodecahedron, Perspective (graphical), Planar graph, Platonic graph, Platonic solid, Polytope compound, Projection (linear algebra), Quasicrystal, Radius, Rectification (geometry), Regular 4-polytope, Regular graph, Regular icosahedron, Regular polygon, Regular polyhedron, Reptiles (M. C. Escher), Rhombic dodecahedron, Role-playing game, Roman dodecahedron, Salvador Dalí, Schläfli symbol, Schlegel diagram, Small ditrigonal icosidodecahedron, Small stellated dodecahedron, Snub dodecahedron, Space diagonal, Sphere, Spherical polyhedron, Stellation, Stereographic projection, Symmetric graph, Tangent, The Phantom Tollbooth, The Sacrament of the Last Supper, Theaetetus (dialogue), Timaeus (dialogue), Truncated dodecahedron, Truncated trapezohedron, Truncation (geometry), Uniform polyhedron compound, Uniform star polyhedron, Vertex arrangement, Vertex configuration, Vertex figure, Volume, VRML, William Rowan Hamilton, 120-cell, 20th-century art, 6-cube, 6-demicube. Expand index (64 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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Alternating group

In mathematics, an alternating group is the group of even permutations of a finite set.

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Apothem

The apothem (sometimes abbreviated as apo) of a regular polygon is a line segment from the center to the midpoint of one of its sides.

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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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Avant-garde metal

Avant-garde metal (or experimental metal) is a subgenre of heavy metal music loosely defined by use of experimentation and innovative, avant-garde elements, including non-standard and unconventional sounds, instruments, song structures, playing styles, and vocal techniques.

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Bertrand Russell

Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British philosopher, logician, mathematician, historian, writer, social critic, political activist, and Nobel laureate.

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Bilunabirotunda

In geometry, the bilunabirotunda is one of the Johnson solids (J91).

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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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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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Compound of five cubes

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

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Compound of five tetrahedra

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

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Compound of ten tetrahedra

The compound of ten tetrahedra is one of the five regular polyhedral compounds.

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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 group

In mathematics, a Coxeter group, named after H. S. M. Coxeter, is an abstract group that admits a formal description in terms of reflections (or kaleidoscopic mirrors).

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Crystal habit

In mineralogy, crystal habit is the characteristic external shape of an individual crystal or crystal group.

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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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Cyclic group

In algebra, a cyclic group or monogenous group is a group that is generated by a single element.

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Diamond

Diamond is a solid form of carbon with a diamond cubic crystal structure.

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Dihedral angle

A dihedral angle is the angle between two intersecting planes.

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Direct product of groups

In group theory, the direct product is an operation that takes two groups and and constructs a new group, usually denoted.

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Distance (graph theory)

In the mathematical field of graph theory, the distance between two vertices in a graph is the number of edges in a shortest path (also called a graph geodesic) connecting them.

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Distance-regular graph

In mathematics, a distance-regular graph is a regular graph such that for any two vertices v and w, the number of vertices at distance j from v and at distance k from w depends only upon j, k, and i.

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Distance-transitive graph

In the mathematical field of graph theory, a distance-transitive graph is a graph such that, given any two vertices v and w at any distance i, and any other two vertices x and y at the same distance, there is an automorphism of the graph that carries v to x and w to y.

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Ditrigonal dodecadodecahedron

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

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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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Face diagonal

In geometry, a face diagonal of a polyhedron is a diagonal on one of the faces, in contrast to a space diagonal passing through the interior of the polyhedron.

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Florian Cajori

Florian Cajori (February 28, 1859 – August 14 or 15, 1930) was a Swiss-American historian of mathematics.

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Garnet

Garnets are a group of silicate minerals that have been used since the Bronze Age as gemstones and abrasives.

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Generalized Petersen graph

In graph theory, the generalized Petersen graphs are a family of cubic graphs formed by connecting the vertices of a regular polygon to the corresponding vertices of a star polygon.

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Gerard Caris

Gerard Caris (born 20 March 1925) is a Dutch sculptor and artist who has pursued a single motif throughout the course of his artistic career, the pentagon.

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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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Graph (discrete mathematics)

In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".

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Graph automorphism

In the mathematical field of graph theory, an automorphism of a graph is a form of symmetry in which the graph is mapped onto itself while preserving the edge–vertex connectivity.

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Graph coloring

In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints.

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Gravitation (M. C. Escher)

Gravitation (also known as Gravity) is a mixed media work by the Dutch artist M. C. Escher completed in June 1952.

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Great ditrigonal icosidodecahedron

In geometry, the great ditrigonal icosidodecahedron is a nonconvex uniform polyhedron, indexed as U47.

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Great dodecahedron

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

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Great stellated dodecahedron

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

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Hamiltonian path

In the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once.

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Hellenistic period

The Hellenistic period covers the period of Mediterranean history between the death of Alexander the Great in 323 BC and the emergence of the Roman Empire as signified by the Battle of Actium in 31 BC and the subsequent conquest of Ptolemaic Egypt the following year.

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Iamblichus

Iamblichus (Ἰάμβλιχος, c. AD 245 – c. 325), was a Syrian Neoplatonist philosopher of Arab origin.

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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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Icosian game

The icosian game is a mathematical game invented in 1857 by William Rowan Hamilton.

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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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Immersive Media

Immersive Media Company (IMC) is a digital imaging company specializing in spherical immersive video.

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Inverse trigonometric functions

In mathematics, the inverse trigonometric functions (occasionally also called arcus functions, antitrigonometric functions or cyclometric functions) are the inverse functions of the trigonometric functions (with suitably restricted domains).

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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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Jean-Pierre Luminet

Jean-Pierre Luminet (born 3 June 1951) is a French astrophysicist, writer and poet, specialized in black holes and cosmology.

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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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K-vertex-connected graph

In graph theory, a connected graph G is said to be k-vertex-connected (or k-connected) if it has more than k vertices and remains connected whenever fewer than k vertices are removed.

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Kepler–Poinsot polyhedron

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

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M. C. Escher

Maurits Cornelis Escher (17 June 1898 – 27 March 1972) was a Dutch graphic artist who made mathematically-inspired woodcuts, lithographs, and mezzotints.

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Mathematical game

A mathematical game is a game whose rules, strategies, and outcomes are defined by clear mathematical parameters.

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Megaminx

The Megaminx is a dodecahedron-shaped puzzle similar to the Rubik's Cube.

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N-skeleton

In mathematics, particularly in algebraic topology, the of a topological space X presented as a simplicial complex (resp. CW complex) refers to the subspace Xn that is the union of the simplices of X (resp. cells of X) of dimensions In other words, given an inductive definition of a complex, the is obtained by stopping at the.

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Net (polyhedron)

In geometry a net of a polyhedron is an arrangement of edge-joined polygons in the plane which can be folded (along edges) to become the faces of the polyhedron.

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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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Orthographic projection

Orthographic projection (sometimes orthogonal projection), is a means of representing three-dimensional objects in two dimensions.

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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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Pentagonal trapezohedron

The pentagonal trapezohedron or deltohedron is the third in an infinite series of face-transitive polyhedra which are dual polyhedra to the antiprisms.

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Pentakis dodecahedron

In geometry, a pentakis dodecahedron or kisdodecahedron is a dodecahedron with a pentagonal pyramid covering each face; that is, it is the Kleetope of the dodecahedron.

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Perspective (graphical)

Perspective (from perspicere "to see through") in the graphic arts is an approximate representation, generally on a flat surface (such as paper), of an image as it is seen by the eye.

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Planar graph

In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints.

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Platonic graph

In the mathematical field of graph theory, a Platonic graph is a graph that has one of the Platonic solids as its skeleton.

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Platonic solid

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

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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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Projection (linear algebra)

In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that.

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Quasicrystal

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

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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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Regular 4-polytope

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

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Regular graph

In graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. every vertex has the same degree or valency.

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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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Reptiles (M. C. Escher)

Reptiles is a lithograph print by the Dutch artist M. C. Escher first printed in March 1943.

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Rhombic dodecahedron

In geometry, the rhombic dodecahedron is a convex polyhedron with 12 congruent rhombic faces.

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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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Roman dodecahedron

A Roman dodecahedron is a small hollow object made of bronze or stone, with a dodecahedral shape: twelve flat pentagonal faces, each face having a circular hole of varying diameter in the middle, the holes connecting to the hollow center.

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Salvador Dalí

Salvador Domingo Felipe Jacinto Dalí i Domènech, 1st Marquess of Dalí de Púbol (11 May 190423 January 1989), known professionally as Salvador Dalí, was a prominent Spanish surrealist born in Figueres, Catalonia, Spain.

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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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Schlegel diagram

In geometry, a Schlegel diagram is a projection of a polytope from R^d into R^ through a point beyond one of its facets or faces.

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Small ditrigonal icosidodecahedron

In geometry, the small ditrigonal icosidodecahedron is a nonconvex uniform polyhedron, indexed as U30.

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Small stellated dodecahedron

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

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Snub dodecahedron

In geometry, the snub dodecahedron, or snub icosidodecahedron, is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed by two or more types of regular polygon faces.

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Space diagonal

In geometry a space diagonal (also interior diagonal or body diagonal) of a polyhedron is a line connecting two vertices that are not on the same face.

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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 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.

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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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Stereographic projection

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

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Symmetric graph

In the mathematical field of graph theory, a graph G is symmetric (or arc-transitive) if, given any two pairs of adjacent vertices u1—v1 and u2—v2 of G, there is an automorphism such that In other words, a graph is symmetric if its automorphism group acts transitively upon ordered pairs of adjacent vertices (that is, upon edges considered as having a direction).

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Tangent

In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point.

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The Phantom Tollbooth

The Phantom Tollbooth is a children's fantasy adventure novel written by Norton Juster with illustrations by Jules Feiffer, published in 1961 by Random House (USA).

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The Sacrament of the Last Supper

The Sacrament of the Last Supper is a painting by Salvador Dalí.

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Theaetetus (dialogue)

The Theaetetus (Θεαίτητος) is one of Plato's dialogues concerning the nature of knowledge, written circa 369 BC.

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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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Truncated dodecahedron

In geometry, the truncated dodecahedron is an Archimedean solid.

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Truncated trapezohedron

An n-gonal truncated trapezohedron is a polyhedron formed by a n-gonal trapezohedron with n-gonal pyramids truncated from its two polar axis vertices.

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Truncation (geometry)

In geometry, a truncation is an operation in any dimension that cuts polytope vertices, creating a new facet in place of each vertex.

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Uniform polyhedron compound

A uniform polyhedron compound is a polyhedral compound whose constituents are identical (although possibly enantiomorphous) uniform polyhedra, in an arrangement that is also uniform: the symmetry group of the compound acts transitively on the compound's vertices.

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Uniform star polyhedron

In geometry, a uniform star polyhedron is a self-intersecting uniform polyhedron.

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Vertex arrangement

In geometry, a vertex arrangement is a set of points in space described by their relative positions.

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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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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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VRML

VRML (Virtual Reality Modeling Language, pronounced vermal or by its initials, originally—before 1995—known as the Virtual Reality Markup Language) is a standard file format for representing 3-dimensional (3D) interactive vector graphics, designed particularly with the World Wide Web in mind.

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William Rowan Hamilton

Sir William Rowan Hamilton MRIA (4 August 1805 – 2 September 1865) was an Irish mathematician who made important contributions to classical mechanics, optics, and algebra.

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120-cell

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

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20th-century art

20th-century art—and what it became as modern art—began with modernism in the late 19th century.

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6-cube

In geometry, a 6-cube is a six-dimensional hypercube with 64 vertices, 192 edges, 240 square faces, 160 cubic cells, 60 tesseract 4-faces, and 12 5-cube 5-faces.

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6-demicube

In geometry, a 6-demicube or demihexteract is a uniform 6-polytope, constructed from a 6-cube (hexeract) with alternated vertices removed.

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Dodecahedral graph, Order-3 pentagonal tiling, Pentagonal Dodecahedron, Spherical dodecahedron, Truncated small stellated dodecahedron.

References

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

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