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|bgcolor=#e7dcc3|[[Schläfli symbol]]||t_0,1{3^[9]} ...dcc3|[[Coxeter notation|Symmetry]]||<math>{\tilde{A}}_8</math>×2, [[3^[9]]] ...

|bgcolor=#e7dcc3|Type||[[Uniform 9-polytope#Regular and uniform honeycombs|Uniform honeycomb]] |bgcolor=#e7dcc3|[[Schläfli symbol]]||{3^[9]} ...

{{Short description|Polytope combining two smaller polytopes}} ...ng facet in the Blaschke sum is the sum of the measures from the two given polytopes.{{r|grunbaum}} ...

|bgcolor=#e7dcc3|Type||[[9-polytope#Regular_and_uniform_honeycombs|Uniform tessellation]] It is created by a [[Wythoff construction]] upon a set of 9 [[hyperplane]] mirrors in 8-dimensional space. ...

|bgcolor=#e7dcc3|Type||[[9-polytope#Regular_and_uniform_honeycombs|Uniform tessellation]] It is created by a [[Wythoff construction]] upon a set of 9 [[hyperplane]] mirrors in 8-dimensional space. ...

|[[File:9-cube t8.svg|100px]]<BR>[[9-orthoplex]]<BR>{{CDD|node|4|node|3|node|3|node|3|node|3|node|3|node|3|node| |[[File:9-cube t7.svg|100px]]<BR>Rectified 9-orthoplex<BR>{{CDD|node|4|node|3|node|3|node|3|node|3|node|3|node|3|node_1| ...

...o key tools: shellability and ''h''-vectors.}}</ref> and strengthened from polytopes to subdivisions of a sphere in 1975 by [[Richard P. Stanley]]. ==Cyclic polytopes== ...

...uoprism]] is a proprism as the product of two orthogonal triangles, having 9 squares between pairs of edges of 2 sets of 3 triangles, and 18 vertices, a ...is a [[polytope]] resulting from the [[Cartesian product]] of two or more polytopes, each of two dimensions or higher. The term was coined by [[John Horton Con ...

...eract ortho petrie.svg|30px]]<br>512 [[9-simplex|{3⁸}]] [[Image:9-simplex t0.svg|25px]] |colspan=2|[[Rectified 9-simplex]]<br>[[File:Rectified 9-simplex.png|40px]] ...

...al unrelated results of Minkowski.{{r|grunbaum}} The Minkowski problem for polytopes should also be distinguished from the [[Minkowski problem]], on specifying ...ape of this polytope is uniquely determined by this information: every two polytopes that give rise to the same set of vectors are [[Translation (geometry)|tran ...

...rve]] in '''R'''^''d'', where ''n'' is greater than ''d''. These polytopes were studied by [[Constantin Carathéodory]], [[David Gale]], [[Theodore Mot The Gale evenness condition<ref>{{cite book |title=Lectures on Polytopes |url=https://archive.org/details/lecturesonpolyto00zieg_081 |url-access=lim ...

...rtices of a [[8-cube honeycomb]].<ref>Coxeter, '''Regular and Semi-Regular Polytopes III''', (1988), p318</ref> Its facets are [[8-demicube]]s h{4,3⁶ ** (Paper 24) H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes III'', [Math. Zeit. 200 (1988) 3-45] See p318 [https://books.google.com/boo ...

...by an [[edge (geometry)|edge]], forming a [[complete graph]]. 2-neighborly polytopes with more than four vertices may exist only in spaces of four or more dimen | title = Convex Polytopes ...

{{DISPLAYTITLE:E₉ honeycomb}} ...>9</sub> honeycomb''' is a tessellation of uniform polytopes in hyperbolic 9-dimensional space. <math>{\bar{T}}_9</math>, also (E₁₀) is a par ...

|9 [[omnitruncated 8-simplex]] |9 ...

There are unique 3 degrees of rectifications in regular 8-polytopes. Vertices of the rectified 8-simplex are located at the edge-centers of the ...is construction is based on [[Facet (geometry)|facets]] of the [[rectified 9-orthoplex]]. ...

| title = The number of faces of centrally-symmetric polytopes ...have four vertices, four edges, and one polygon: {{nowrap|4 + 4 + 1 {{=}} 9 {{=}} 3²}}. A [[cube]] is centrally symmetric, and has 8 vertice ...

...de|3|3node|3|3node}}, order 648 at each cell.<ref>Coxeter, Complex Regular Polytopes, p.134</ref> ...uration (polytope)|configuration matrix]] is:<ref>Coxeter, Complex Regular polytopes, p.132</ref> ...

|bgcolor=#e7dcc3|[[Schläfli symbol]]||{3^[9]} = 0_[9] ...dcc3|[[Coxeter notation|Symmetry]]||<math>{\tilde{A}}_8</math>×2, [[3^[9]]] ...

...irror on an order-4 [[Peak (geometry)|peak]].<ref>Regular and semi-regular polytopes III, p.318-319</ref> | h&delta;₉ ...