Faster access than browser!
68 relations: Archimedean graph, Archimedean solid, Buckminster Fuller, Cartesian coordinate system, Compound of five octahedra, Compound of five tetrahemihexahedra, Conformal map, Coxeter element, Cuboctahedron, Decagon, Dihedral group, Dodecadodecahedron, Dodecahedron, Dual polyhedron, Fundamental domain, Geometry, Golden ratio, Graph theory, Great circle, Great dodecahemicosahedron, Great dodecahemidodecahedron, Great icosidodecahedron, Great icosihemidodecahedron, Great truncated icosidodecahedron, Hamiltonian path, Harold Scott MacDonald Coxeter, Hypersphere, Icosahedron, Johnson solid, Mathematics, N-skeleton, Orbifold notation, Orthographic projection, Oxford University Press, Parity of a permutation, Pentagon, Pentagonal orthobirotunda, Pentagonal rotunda, Polyhedron, Projection (linear algebra), Quartic graph, Quasiregular polyhedron, Rectification (geometry), Regular graph, Regular polytope, Regular Polytopes (book), Rhombic triacontahedron, Rhombicosidodecahedron, Schlegel diagram, Small dodecahemicosahedron, ..., Small dodecahemidodecahedron, Small icosihemidodecahedron, Spherical polyhedron, Stellation, Stereographic projection, Tetrahedral symmetry, Triangle, Truncated cube, Truncated icosidodecahedron, Uniform polyhedron compound, Uniform star polyhedron, Vertex (graph theory), Vertex arrangement, Vertex configuration, Wire-frame model, Wythoff construction, 31 great circles of the spherical icosahedron, 600-cell. Expand index (18 more) »
Archimedean graph
In the mathematical field of graph theory, an Archimedean graph is a graph that forms the skeleton of one of the Archimedean solids.
New!!: Icosidodecahedron and Archimedean graph · See more »
Archimedean solid
In geometry, an Archimedean solid is one of the 13 solids first enumerated by Archimedes.
New!!: Icosidodecahedron and Archimedean solid · See more »
Buckminster Fuller
Richard Buckminster "Bucky" Fuller (July 12, 1895 – July 1, 1983) was an American architect, systems theorist, author, designer, inventor and futurist.
New!!: Icosidodecahedron and Buckminster Fuller · See more »
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.
New!!: Icosidodecahedron and Cartesian coordinate system · See more »
Compound of five octahedra
The compound of five octahedra is one of the five regular polyhedron compounds.
New!!: Icosidodecahedron and Compound of five octahedra · See more »
Compound of five tetrahemihexahedra
A compound of five tetrahemihexahedra is a uniform polyhedron compound and a symmetric arrangement of five tetrahemihexahedra.
New!!: Icosidodecahedron and Compound of five tetrahemihexahedra · See more »
Conformal map
In mathematics, a conformal map is a function that preserves angles locally.
New!!: Icosidodecahedron and Conformal map · See more »
Coxeter element
In mathematics, the Coxeter number h is the order of a Coxeter element of an irreducible Coxeter group.
New!!: Icosidodecahedron and Coxeter element · See more »
Cuboctahedron
In geometry, a cuboctahedron is a polyhedron with 8 triangular faces and 6 square faces.
New!!: Icosidodecahedron and Cuboctahedron · See more »
Decagon
In geometry, a decagon is a ten-sided polygon or 10-gon.
New!!: Icosidodecahedron and Decagon · See more »
Dihedral group
In mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections.
New!!: Icosidodecahedron and Dihedral group · See more »
Dodecadodecahedron
In geometry, the dodecadodecahedron is a nonconvex uniform polyhedron, indexed as U36.
New!!: Icosidodecahedron 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!!: Icosidodecahedron 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!!: Icosidodecahedron and Dual polyhedron · See more »
Fundamental domain
Given a topological space and a group acting on it, the images of a single point under the group action form an orbit of the action.
New!!: Icosidodecahedron and Fundamental domain · See more »
Geometry
Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.
New!!: Icosidodecahedron and Geometry · See more »
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.
New!!: Icosidodecahedron and Golden ratio · See more »
Graph theory
In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.
New!!: Icosidodecahedron and Graph theory · 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!!: Icosidodecahedron and Great circle · See more »
Great dodecahemicosahedron
In geometry, the great dodecahemicosahedron is a nonconvex uniform polyhedron, indexed as U65.
New!!: Icosidodecahedron and Great dodecahemicosahedron · See more »
Great dodecahemidodecahedron
In geometry, the great dodecahemidodecahedron is a nonconvex uniform polyhedron, indexed as U70.
New!!: Icosidodecahedron and Great dodecahemidodecahedron · See more »
Great icosidodecahedron
In geometry, the great icosidodecahedron is a nonconvex uniform polyhedron, indexed as U54.
New!!: Icosidodecahedron and Great icosidodecahedron · See more »
Great icosihemidodecahedron
In geometry, the great icosihemidodecahedron is a nonconvex uniform polyhedron, indexed as U71.
New!!: Icosidodecahedron and Great icosihemidodecahedron · See more »
Great truncated icosidodecahedron
In geometry, the great truncated icosidodecahedron or great quasitruncated icosidodecahedron is a nonconvex uniform polyhedron, indexed as U68.
New!!: Icosidodecahedron and Great truncated icosidodecahedron · See more »
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.
New!!: Icosidodecahedron and Hamiltonian path · 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!!: Icosidodecahedron and Harold Scott MacDonald Coxeter · See more »
Hypersphere
In geometry of higher dimensions, a hypersphere is the set of points at a constant distance from a given point called its center.
New!!: Icosidodecahedron and Hypersphere · See more »
Icosahedron
In geometry, an icosahedron is a polyhedron with 20 faces.
New!!: Icosidodecahedron and Icosahedron · See more »
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.
New!!: Icosidodecahedron and Johnson solid · See more »
Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
New!!: Icosidodecahedron and Mathematics · See more »
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.
New!!: Icosidodecahedron and N-skeleton · See more »
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.
New!!: Icosidodecahedron and Orbifold notation · See more »
Orthographic projection
Orthographic projection (sometimes orthogonal projection), is a means of representing three-dimensional objects in two dimensions.
New!!: Icosidodecahedron and Orthographic projection · See more »
Oxford University Press
Oxford University Press (OUP) is the largest university press in the world, and the second oldest after Cambridge University Press.
New!!: Icosidodecahedron and Oxford University Press · See more »
Parity of a permutation
In mathematics, when X is a finite set of at least two elements, the permutations of X (i.e. the bijective functions from X to X) fall into two classes of equal size: the even permutations and the odd permutations.
New!!: Icosidodecahedron and Parity of a permutation · 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!!: Icosidodecahedron and Pentagon · See more »
Pentagonal orthobirotunda
In geometry, the pentagonal orthobirotunda is one of the Johnson solids (J34).
New!!: Icosidodecahedron and Pentagonal orthobirotunda · See more »
Pentagonal rotunda
In geometry, the pentagonal rotunda is one of the Johnson solids (J6).
New!!: Icosidodecahedron and Pentagonal rotunda · 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!!: Icosidodecahedron and Polyhedron · See more »
Projection (linear algebra)
In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that.
New!!: Icosidodecahedron and Projection (linear algebra) · See more »
Quartic graph
In the mathematical field of graph theory, a quartic graph is a graph where all vertices have degree 4.
New!!: Icosidodecahedron and Quartic graph · 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!!: Icosidodecahedron and Quasiregular polyhedron · See more »
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.
New!!: Icosidodecahedron and Rectification (geometry) · See more »
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.
New!!: Icosidodecahedron and Regular graph · 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!!: Icosidodecahedron and Regular polytope · See more »
Regular Polytopes (book)
Regular Polytopes is a mathematical geometry book written by Canadian mathematician Harold Scott MacDonald Coxeter.
New!!: Icosidodecahedron and Regular Polytopes (book) · See more »
Rhombic triacontahedron
In geometry, the rhombic triacontahedron, sometimes simply called the triacontahedron as it is the most common thirty-faced polyhedron, is a convex polyhedron with 30 rhombic faces.
New!!: Icosidodecahedron and Rhombic triacontahedron · See more »
Rhombicosidodecahedron
In geometry, the rhombicosidodecahedron, or small rhombicosidodecahedron, is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces.
New!!: Icosidodecahedron and Rhombicosidodecahedron · See more »
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.
New!!: Icosidodecahedron and Schlegel diagram · See more »
Small dodecahemicosahedron
In geometry, the small dodecahemicosahedron is a nonconvex uniform polyhedron, indexed as U62.
New!!: Icosidodecahedron and Small dodecahemicosahedron · See more »
Small dodecahemidodecahedron
In geometry, the small dodecahemidodecahedron is a nonconvex uniform polyhedron, indexed as U51.
New!!: Icosidodecahedron and Small dodecahemidodecahedron · See more »
Small icosihemidodecahedron
In geometry, the small icosihemidodecahedron is a uniform star polyhedron, indexed as U49.
New!!: Icosidodecahedron and Small icosihemidodecahedron · 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!!: Icosidodecahedron and Spherical 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!!: Icosidodecahedron and Stellation · See more »
Stereographic projection
In geometry, the stereographic projection is a particular mapping (function) that projects a sphere onto a plane.
New!!: Icosidodecahedron and Stereographic projection · See more »
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.
New!!: Icosidodecahedron and Tetrahedral symmetry · See more »
Triangle
A triangle is a polygon with three edges and three vertices.
New!!: Icosidodecahedron and Triangle · See more »
Truncated cube
In geometry, the truncated cube, or truncated hexahedron, is an Archimedean solid.
New!!: Icosidodecahedron and Truncated cube · See more »
Truncated icosidodecahedron
In geometry, the truncated icosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed by two or more types of regular polygon faces.
New!!: Icosidodecahedron and Truncated icosidodecahedron · See more »
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.
New!!: Icosidodecahedron and Uniform polyhedron compound · See more »
Uniform star polyhedron
In geometry, a uniform star polyhedron is a self-intersecting uniform polyhedron.
New!!: Icosidodecahedron and Uniform star polyhedron · See more »
Vertex (graph theory)
In mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph consists of a set of vertices and a set of arcs (ordered pairs of vertices).
New!!: Icosidodecahedron and Vertex (graph theory) · See more »
Vertex arrangement
In geometry, a vertex arrangement is a set of points in space described by their relative positions.
New!!: Icosidodecahedron and Vertex arrangement · See more »
Vertex configuration
In geometry, a vertex configuration by Walter Steurer, Sofia Deloudi, (2009) pp.
New!!: Icosidodecahedron and Vertex configuration · See more »
Wire-frame model
A wire-frame model is a visual presentation of a 3-dimensional (3D) or physical object used in 3D computer graphics.
New!!: Icosidodecahedron and Wire-frame model · See more »
Wythoff construction
In geometry, a Wythoff construction, named after mathematician Willem Abraham Wythoff, is a method for constructing a uniform polyhedron or plane tiling.
New!!: Icosidodecahedron and Wythoff construction · See more »
31 great circles of the spherical icosahedron
In geometry, the 31 great circles of the spherical icosahedron is an arrangement of 31 great circles in icosahedral symmetry.
New!!: Icosidodecahedron and 31 great circles of the spherical icosahedron · See more »
600-cell
In geometry, the 600-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol.
New!!: Icosidodecahedron and 600-cell · See more »
Redirects here:
Icosadodecahedron, Icosidodecahedral graph, Id (geometry), Pentagonal gyrobirotunda, Rectified dodecahedron.
References
[1] https://en.wikipedia.org/wiki/Icosidodecahedron
