A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags. A regular polyhedron is highly symmetrical, being all of edge-transitive... 32 KB (3,118 words) - 14:26, 10 April 2024 |
Platonic solid (redirect from Convex regular polyhedron) geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent... 53 KB (5,532 words) - 21:46, 29 April 2024 |
In geometry, a polyhedron (pl.: polyhedra or polyhedrons; from Greek πολύ (poly-) 'many', and ἕδρον (-hedron) 'base, seat') is a three-dimensional shape... 86 KB (9,737 words) - 18:21, 23 March 2024 |
In geometry, the regular icosahedron (or simply icosahedron) is a convex polyhedron that can be constructed from pentagonal antiprism by attaching two... 35 KB (3,685 words) - 03:37, 19 April 2024 |
In geometry, a uniform polyhedron has regular polygons as faces and is vertex-transitive (i.e., there is an isometry mapping any vertex onto any other)... 66 KB (2,540 words) - 22:41, 20 March 2024 |
Johnson solid (redirect from Face-regular polyhedron) In geometry, a Johnson solid is a strictly convex polyhedron each face of which is a regular polygon. There is no requirement that each face must be the... 52 KB (1,743 words) - 13:00, 17 March 2024 |
A geodesic polyhedron is a convex polyhedron made from triangles. They usually have icosahedral symmetry, such that they have 6 triangles at a vertex... 17 KB (1,141 words) - 16:48, 4 May 2024 |
for a regular polygon). A quasiregular polyhedron is a uniform polyhedron which has just two kinds of face alternating around each vertex. A regular polyhedron... 30 KB (3,201 words) - 23:26, 14 April 2024 |
Dodecahedron (section Regular dodecahedron) duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagons as faces, which... 28 KB (2,027 words) - 01:06, 24 April 2024 |
In geometry, every polyhedron is associated with a second dual structure, where the vertices of one correspond to the faces of the other, and the edges... 19 KB (2,221 words) - 09:11, 25 January 2024 |
Archimedean solid (redirect from Archimedean polyhedron) prisms and antiprisms. The pseudorhombicuboctahedron is an extra polyhedron with regular faces and congruent vertices, but it is not generally counted as... 26 KB (1,309 words) - 05:59, 3 November 2023 |
Polytope compound (redirect from Regular compound polyhedron) This polyhedron can be used as the core for a set of stellations. A regular polyhedral compound can be defined as a compound which, like a regular polyhedron... 25 KB (1,425 words) - 16:50, 28 November 2023 |
called polyhedra: A regular polyhedron with Schläfli symbol {p, q}, Coxeter diagrams , has a regular face type {p}, and regular vertex figure {1}. A... 97 KB (5,294 words) - 16:02, 26 March 2024 |
Abstract polytope (redirect from Abstract regular polyhedron) versa. For example, a traditional polytope is regular if all its facets and vertex figures are regular, but this is not necessarily so for an abstract... 34 KB (4,530 words) - 22:20, 16 September 2023 |
Octahedron (redirect from Regular octahedron) : octahedra or octahedrons) is a polyhedron with eight faces. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed... 26 KB (2,748 words) - 01:59, 14 March 2024 |
Prism (geometry) (section Regular prism) In geometry, a prism is a polyhedron comprising an n-sided polygon base, a second base which is a translated copy (rigidly moved without rotation) of the... 20 KB (1,852 words) - 05:30, 7 May 2024 |
Icosahedron (section Regular icosahedra) faces meeting around each vertex. Its dual polyhedron is the regular dodecahedron {5, 3} having three regular pentagonal faces around each vertex. The great... 11 KB (874 words) - 02:28, 16 February 2024 |
semiregular polyhedron (or semiregular polytope) is used variously by different authors. In its original definition, it is a polyhedron with regular polygonal... 9 KB (979 words) - 18:13, 15 February 2023 |
Viviani's theorem (section Regular polyhedron) distances. The sum of the distances from any point in the interior of a regular polyhedron to the sides is independent of the location of the point. However... 8 KB (912 words) - 03:40, 31 December 2023 |
which make up a regular icosahedron. A dodecahedron, on the other hand, has twenty vertices, likewise the most a regular polyhedron can have. There are... 15 KB (1,696 words) - 20:42, 10 May 2024 |
10-demicube. Skew polygon Infinite skew polyhedron Abstract regular polytopes, p.7, p.17 Coxeter, Regular and Semi-Regular Polytopes II 2.34) Coxeter and Moser... 14 KB (747 words) - 22:50, 29 May 2022 |
Tetrahedron (redirect from Regular tetrahedron) tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertices... 73 KB (8,822 words) - 15:51, 7 May 2024 |
submersion Regular polygons, polygons with all sides and angles equal Regular polyhedron, a generalization of a regular polygon to higher dimensions Regular polytope... 7 KB (962 words) - 21:20, 2 December 2023 |
Cube (redirect from Regular hexahedron) octahedron. It has cubical or octahedral symmetry, and is the only convex polyhedron whose faces are all squares. Its generalization for higher-dimensional... 19 KB (1,778 words) - 20:27, 29 February 2024 |
Steinitz's theorem (redirect from Skeletal regular polyhedron) convex polyhedron forms a 3-connected planar graph, and every 3-connected planar graph can be represented as the graph of a convex polyhedron. For this... 50 KB (5,937 words) - 15:50, 19 November 2023 |
Rectification (geometry) (section Regular polygons) The rectification of any regular self-dual polyhedron or tiling will result in another regular polyhedron or tiling with a tiling order of 4, for example... 15 KB (889 words) - 05:27, 8 July 2023 |
In geometry, a net of a polyhedron is an arrangement of non-overlapping edge-joined polygons in the plane which can be folded (along edges) to become the... 12 KB (1,420 words) - 15:07, 4 March 2024 |