simplicial, polytope, confused, with, simple, polytope, geometry, simplicial, polytope, polytope, whose, facets, simplices, example, simplicial, polyhedron, three, dimensions, contains, only, triangular, faces, corresponds, steinitz, theorem, maximal, planar, . Not to be confused with Simple 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 1 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 Contents 1 Examples 2 See also 3 Notes 4 ReferencesExamples editSimplicial polyhedra include Bipyramids Gyroelongated dipyramids 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 triacontahedronSimplicial tilings Regular triangular tiling Laves tilings tetrakis square tiling triakis triangular tiling kisrhombille tilingSimplicial 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 honeycombSimplicial higher polytope families simplex cross polytope Orthoplex See also editSimplicial complex Delaunay triangulationNotes edit Polyhedra Peter R Cromwell 1997 p 341 References editCromwell Peter R 1997 Polyhedra Cambridge University Press ISBN 0 521 66405 5 nbsp This geometry related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Simplicial polytope amp oldid 1117244656, wikipedia, wiki, book, books, library,
