• Source: 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.




Examples


Simplicial polyhedra include:

Bipyramids
Gyroelongated bipyramids
Deltahedra (equilateral triangles)
Platonic
tetrahedron, octahedron, icosahedron
Johnson solids:
triangular bipyramid, pentagonal bipyramid, snub disphenoid, triaugmented triangular prism, gyroelongated square dipyramid
Catalan solids:
triakis tetrahedron, triakis octahedron, tetrakis hexahedron, disdyakis dodecahedron, triakis icosahedron, pentakis dodecahedron, disdyakis triacontahedron
Simplicial tilings:

Regular:
triangular tiling
Laves tilings:
tetrakis square tiling, triakis triangular tiling, kisrhombille tiling
Simplicial 4-polytopes include:

convex regular 4-polytope
4-simplex, 16-cell, 600-cell
Dual convex uniform honeycombs:
Disphenoid tetrahedral honeycomb
Dual of cantitruncated cubic honeycomb
Dual of omnitruncated cubic honeycomb
Dual of cantitruncated alternated cubic honeycomb
Simplicial higher polytope families:

simplex
cross-polytope (Orthoplex)




See also


Simplicial complex
Delaunay triangulation




Notes






References


Cromwell, Peter R. (1997). Polyhedra. Cambridge University Press. ISBN 0-521-66405-5.

Kata Kunci Pencarian:

• Simplicial polytope
• Simplicial complex
• Euler line
• Polyhedron
• Polytope
• H-vector
• Simple polytope
• Cyclic polytope
• Dehn–Sommerville equations
• Circumcenter of mass