The octahedron is an example of a simplicial polyhedron.
A simplicial polyhedron is a polyhedron , all of whose faces are simplexes . In particular, a three-dimensional polyhedron is simplicial if all its faces are triangles.
Properties
- The graph of a three-dimensional simplicial polyhedron is a maximally flat graph , i.e., if you add any one edge to it, then it ceases to be flat.
- Simplicial polyhedra are dual simple .
- In particular, for the simplicial polyhedra the variant of the Dehn - Somerville equations holds
- A polyhedron is simultaneously simple and simplicial is a simplex or polygon .
Examples
- Bipyramid
- Regular Polyhedrons
- tetrahedron , octahedron , icosahedron
See also
- Simplicial complex
- Delaunay Triangulation