Simplicial polytope

Tetrahedron : all faces are triangles

In geometry , a simplicial polytope is a polytope whose faces are simplexes .

For example, a tetrahedron is a simplicial polytope because its faces are 2-dimensional simplices (triangles). The cube is not a simplicial polytope because its faces are not triangles, but rectangles.

Examples

1-dimensional simplicial polytopes

• Polygons

2-dimensional simplicial polytopes

• Tetrahedron
• Double pyramids , especially octahedra
• Deltahedra , especially icosahedron

3-dimensional simplicial polytopes

• Pentachoron
• 16-cell (Hexadekachor)

Higher-dimensional simplicial polytopes

• n-simplex
• Cross polytopes