Concept

Simplicial polytope

In geometry, a simplicial polytope is a polytope whose facets are all simplices. For example, a simplicial polyhedron in three dimensions contains only triangular faces and corresponds via Steinitz's theorem to a maximal planar graph. They are topologically dual to simple polytopes. Polytopes which are both simple and simplicial are either simplices or two-dimensional polygons.

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https://en.wikipedia.org/wiki/Simplicial_polytope

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Official source

https://en.wikipedia.org/wiki/Simplicial_polytope

About this result

Related courses (1)

MATH-124: Geometry for architects I

Related lectures (4)

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Explores the concept of symmetry in various geometric transformations.

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Covers the adjunction between simplicial sets and simplicially enriched categories, including preservation of inclusions and construction of homotopy categories.

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Related concepts (5)

Snub disphenoid

In geometry, the snub disphenoid, Siamese dodecahedron, triangular dodecahedron, trigonal dodecahedron, or dodecadeltahedron is a convex polyhedron with twelve equilateral triangles as its faces. It is not a regular polyhedron because some vertices have four faces and others have five. It is a dodecahedron, one of the eight deltahedra (convex polyhedra with equilateral triangle faces), and is the 84th Johnson solid (non-uniform convex polyhedra with regular faces).

Facet (geometry)

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Polyhedral combinatorics

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