• Thumbnail for Polyhedron
    In geometry, a polyhedron (pl.: polyhedra or polyhedrons; from Greek πολύ (poly-)  'many' and ἕδρον (-hedron)  'base, seat') is a three-dimensional figure...
    91 KB (10,133 words) - 12:31, 14 December 2024
  • Thumbnail for Dual polyhedron
    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...
    18 KB (2,272 words) - 22:18, 21 August 2024
  • 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 (3,126 words) - 21:09, 19 December 2024
  • Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical...
    54 KB (5,615 words) - 07:53, 22 December 2024
  • Thumbnail for Cube
    three-dimensional solid object bounded by six congruent square faces, a type of polyhedron. It has twelve congruent edges and eight vertices. It is a type of parallelepiped...
    38 KB (4,054 words) - 03:37, 5 November 2024
  • space is called an n-dimensional polyhedron. Polyhedron may also refer to: Polyhedron (magazine), formerly Polyhedron Newszine, a former magazine targeting...
    720 bytes (119 words) - 05:36, 27 May 2024
  • Thumbnail for Goldberg polyhedron
    more specifically in polyhedral combinatorics, a Goldberg polyhedron is a convex polyhedron made from hexagons and pentagons. They were first described...
    12 KB (646 words) - 11:27, 16 December 2024
  • Thumbnail for Geodesic polyhedron
    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) - 04:12, 8 June 2024
  • Thumbnail for Vertex (geometry)
    "reflex". More generally, a vertex of a polyhedron or polytope is convex, if the intersection of the polyhedron or polytope with a sufficiently small sphere...
    8 KB (911 words) - 09:20, 26 November 2024
  • numbers of vertices (corners), edges and faces in the given polyhedron. Any convex polyhedron's surface has Euler characteristic   χ = V − E + F = 2   ....
    29 KB (3,449 words) - 06:08, 16 December 2024
  • Thumbnail for Uniform polyhedron
    In geometry, a uniform polyhedron has regular polygons as faces and is vertex-transitive—there is an isometry mapping any vertex onto any other. It follows...
    66 KB (2,584 words) - 00:49, 16 December 2024
  • Thumbnail for Edge (geometry)
    edges; this square has 4 edges. Every edge is shared by two faces in a polyhedron, like this cube. Every edge is shared by three or more faces in a 4-polytope...
    6 KB (689 words) - 02:13, 16 December 2024
  • Thumbnail for Schönhardt polyhedron
    In geometry, a Schönhardt polyhedron is a polyhedron with the same combinatorial structure as a regular octahedron, but with dihedral angles that are non-convex...
    16 KB (1,709 words) - 14:58, 18 August 2024
  • Polyhedron (formerly Polyhedron Newszine) was a magazine targeting consumers of role-playing games, and originally the official publication of the RPGA...
    9 KB (1,009 words) - 21:57, 30 July 2024
  • Thumbnail for Archimedean solid
    elongated square gyrobicupola or pseudo­rhombi­cub­octa­hedron is an extra polyhedron with regular faces and congruent vertices, but it is not generally counted...
    21 KB (1,761 words) - 22:15, 14 December 2024
  • Thumbnail for Spherical polyhedron
    In geometry, 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...
    11 KB (514 words) - 00:11, 22 October 2024
  • An n-dimensional polyhedron is a geometric object that generalizes the 3-dimensional polyhedron to an n-dimensional space. It is defined as a set of points...
    11 KB (1,578 words) - 11:34, 28 May 2024
  • Thumbnail for Toroidal polyhedron
    In geometry, a toroidal polyhedron is a polyhedron which is also a toroid (a g-holed torus), having a topological genus (g) of 1 or greater. Notable examples...
    12 KB (997 words) - 01:27, 30 April 2024
  • geometry, the Császár polyhedron (Hungarian: [ˈt͡ʃaːsaːr]) is a nonconvex toroidal polyhedron with 14 triangular faces. This polyhedron has no diagonals;...
    8 KB (682 words) - 11:35, 13 March 2024
  • Thumbnail for Net (polyhedron)
    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...
    13 KB (1,435 words) - 22:24, 21 August 2024
  • is a strictly convex polyhedron whose faces are regular polygons. They are sometimes defined to exclude the uniform polyhedrons. There are ninety-two...
    19 KB (1,833 words) - 08:00, 15 October 2024
  • Thumbnail for Szilassi polyhedron
    Szilassi polyhedron is a nonconvex polyhedron, topologically a torus, with seven hexagonal faces. The 14 vertices and 21 edges of the Szilassi polyhedron form...
    6 KB (547 words) - 04:21, 20 November 2024
  • Thumbnail for Ideal polyhedron
    In three-dimensional hyperbolic geometry, an ideal polyhedron is a convex polyhedron all of whose vertices are ideal points, points "at infinity" rather...
    27 KB (3,226 words) - 23:07, 3 November 2024
  • Thumbnail for Truncated tetrahedron
    all of its vertices off, a process known as truncation. The resulting polyhedron has 4 equilateral triangles and 4 regular hexagons, 18 edges, and 12 vertices...
    12 KB (1,225 words) - 05:49, 16 December 2024
  • Thumbnail for Truncated icosahedron
    In geometry, the truncated icosahedron is a polyhedron that can be constructed by truncating all of the regular icosahedron's vertices. Intuitively, it...
    16 KB (1,547 words) - 09:15, 16 December 2024
  • In geometry, a composite polyhedron is a convex polyhedron that produces other polyhedrons when sliced by a plane. Examples can be found in Johnson solids...
    5 KB (431 words) - 02:37, 27 September 2024
  • Thumbnail for Flexible polyhedron
    In geometry, a flexible polyhedron is a polyhedral surface without any boundary edges, whose shape can be continuously changed while keeping the shapes...
    10 KB (907 words) - 12:32, 26 August 2021
  • Thumbnail for Density (polytope)
    In geometry, the density of a star polyhedron is a generalization of the concept of winding number from two dimensions to higher dimensions, representing...
    10 KB (1,171 words) - 08:34, 1 October 2024
  • uniform star polyhedron with Wythoff symbol of the form 3 | p q or ⁠3/2⁠ | p q are ditrigonal, at least if p and q are not 2. Each polyhedron includes two...
    4 KB (274 words) - 08:04, 25 September 2024
  • In geometry, a star polyhedron is a polyhedron which has some repetitive quality of nonconvexity giving it a star-like visual quality. There are two general...
    8 KB (773 words) - 17:52, 14 November 2024