In geometry, a polyhedron (pl.: polyhedra or polyhedrons; from Greek πολύ (poly-)  'many', and ἕδρον (-hedron)  'base, seat') is a three-dimensional shape...

Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical...

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...

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...

space is called an n-dimensional polyhedron. Polyhedron may also refer to: Polyhedron (magazine), formerly Polyhedron Newszine, a former magazine targeting...

of solids: Platonic solid, regular polyhedron, parallelohedron, zonohedron, and plesiohedron. The dual polyhedron of a cube is the regular octahedron...

more specifically in polyhedral combinatorics, a Goldberg polyhedron is a convex polyhedron made from hexagons and pentagons. They were first described...

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...

Szilassi polyhedron is a nonconvex polyhedron, topologically a torus, with seven hexagonal faces. The 14 vertices and 21 edges of the Szilassi polyhedron form...

A geodesic polyhedron is a convex polyhedron made from triangles. They usually have icosahedral symmetry, such that they have 6 triangles at a vertex...

"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...

cube#Generalizations Quasicrystal Regular polyhedron Semiregular polyhedron Toroidal polyhedron Uniform polyhedron Steckles, Katie. "The Unwanted Shape"....

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...

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...

geometry, the Császár polyhedron (Hungarian: [ˈt͡ʃaːsaːr]) is a nonconvex toroidal polyhedron with 14 triangular faces. This polyhedron has no diagonals;...

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...

In geometry, a flexible polyhedron is a polyhedral surface without any boundary edges, whose shape can be continuously changed while keeping the shapes...

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...

numbers of vertices (corners), edges and faces in the given polyhedron. Any convex polyhedron's surface has Euler characteristic   χ = V − E + F = 2   ....

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...

In three-dimensional hyperbolic geometry, an ideal polyhedron is a convex polyhedron all of whose vertices are ideal points, points "at infinity" rather...

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...

A polyhedron model is a physical construction of a polyhedron, constructed from cardboard, plastic board, wood board or other panel material, or, less...

solid object; a three-dimensional solid bounded exclusively by faces is a polyhedron. In more technical treatments of the geometry of polyhedra and higher-dimensional...

or intersphere of a convex polyhedron is a sphere which is tangent to every edge of the polyhedron. Not every polyhedron has a midsphere, but the uniform...

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...

dimension 2 (a plane tiling) or higher, or a polytope of dimension 3 (a polyhedron) or higher, is isohedral or face-transitive if all its faces are the same...

In geometry, a (globally) projective polyhedron is a tessellation of the real projective plane. These are projective analogs of spherical polyhedra – tessellations...

In geometry, an omnitruncated polyhedron is a truncated quasiregular polyhedron. When they are alternated, they produce the snub polyhedra. All omnitruncated...

In geometry, the density of a star polyhedron is a generalization of the concept of winding number from two dimensions to higher dimensions, representing...