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

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...

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

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

A cube is a three-dimensional solid object in geometry. A polyhedron, its eight vertices and twelve straight edges of the same length form six square faces...

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

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...

Polyhedron (formerly Polyhedron Newszine) was a magazine targeting consumers of role-playing games, and originally the official publication of the RPGA...

Szilassi polyhedron is a nonconvex polyhedron, topologically a torus, with seven hexagonal faces. The tetrahedron and the Szilassi polyhedron are the only...

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...

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

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...

constructing another polyhedron. Examples are some of the Johnson solids, the truncated right triangular prism, and Schönhardt polyhedron. A triangular prism...

In geometry, a Kepler–Poinsot polyhedron is any of four regular star polyhedra. They may be obtained by stellating the regular convex dodecahedron and...

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...

dual uniform polyhedron is the dual of a uniform polyhedron. Where a uniform polyhedron is vertex-transitive, a dual uniform polyhedron is face-transitive...

extends facets of a polyhedron to form a new figure. Usually, this is achieved by extending faces or edges and planes of a polyhedron, until they generate...

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...

form a convex polyhedron called its convex hull. A compound is a faceting of its convex hull.[citation needed] Another convex polyhedron is formed by the...

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...

In geometry, an octahedron (pl.: octahedra or octahedrons) is any polyhedron with eight faces. One special case is the regular octahedron, a Platonic solid...

"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...

Archimedean solids are synonymous with the semiregular polyhedron. Yet, the definition of a semiregular polyhedron may also include the infinite prisms and antiprisms...

stellation is the process of extending a polygon in two dimensions, a polyhedron in three dimensions, or, in general, a polytope in n dimensions to form...

given polyhedron. Any convex polyhedron's surface has an Euler characteristic. This equation, stated by Euler in 1758, is known as Euler's polyhedron formula...

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 prism is a polyhedron comprising an n-sided polygon base, a second base which is a translated copy (rigidly moved without rotation) of the...