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!bgcolor=#e7dcc3 colspan=2|Cyclotruncated 7-simplex honeycomb ...30px]]<BR>[[tritruncated 7-simplex|t_2,3{3⁶}]] [[File:7-simplex t23.svg|30px]] ...

|bgcolor=#e7dcc3|Type||[[Uniform 7-polytope#Regular and uniform honeycombs|Uniform honeycomb]] |bgcolor=#e7dcc3|[[Schläfli symbol]]||t_0,1{3^[7]} ...

...implex t23.svg|30px]]<BR>[[Quadritruncated 8-simplex|t_3,4{3⁷}]] [[File:8-simplex t34.svg|30px]] |bgcolor=#e7dcc3|Vertex figure||Elongated 7-simplex antiprism ...

!bgcolor=#e7dcc3 colspan=2|Omnitruncated 7-simplex honeycomb |bgcolor=#e7dcc3|6-face types||[[Omnitruncated 7-simplex|t_0123456{3,3,3,3,3,3}]] ...

...c3|[[Coxeter notation|Symmetry]]||<math>{\tilde{A}}_7</math>×14, [7[3^[7]]] The A{{sup sub|*|6}} lattice (also called A{{sup sub|7|6}}) is the union of seven [[A6 lattice|A₆ lattices]], and has t ...

...ain/johnson.htm#blind|title=Johnson solids, Blind polytopes, and CRFs|work=Polytopes|first=Richard|last=Klitzing|access-date=2022-11-14}}</ref> The set of [[convex uniform 4-polytope]]s (also called semiregular 4-polytopes) are completely known cases, nearly all grouped by their [[Wythoff construc ...

|bgcolor=#e7dcc3|7-face types||[[Omnitruncated 7-simplex|t_01234567{3,3,3,3,3,3,3}]] == Related polytopes and honeycombs == ...

...ub>41</sub>]]'''[[File:Gosset 2 41 petrie.svg|25px]]<BR>[[8-simplex|{3⁷}]][[Image:8-simplex t0.svg|25px]] ...ge:Gosset 2 31 polytope.svg|25px]]<BR>[[7-simplex|{3⁶}]][[Image:7-simplex t0.svg|25px]] ...

{{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}} ...

...2 polytope|1₃₂]]'''[[File:Gosset 1 32 petrie.svg|25px]]<BR>'''[[7-demicube|1₄₁]]'''[[Image:Demihepteract ortho petrie.svg|25px]] ...7dcc3|[[Vertex figure]]||[[birectified 8-simplex]]:<BR>t₂{3⁷} [[File:Birectified 8-simplex.png|25px]] ...

...is construction is based on [[Facet (geometry)|facets]] of the [[rectified 7-orthoplex]]. ...|5-faces||14 total:<BR>7 [[Rectified 5-simplex|t₁{3,3,3,3}]]<BR>7 [[Birectified 5-simplex|t₂{3,3,3,3}]] ...

!bgcolor=#e7dcc3 colspan=2|quarter 7-cubic honeycomb |bgcolor=#e7dcc3|Type||[[Uniform 7-honeycomb]] ...

|[[File:7-cube t0.svg|100px]]<BR>[[7-cube]]<BR>{{CDD|node_1|4|node|3|node|3|node|3|node|3|node|3|node}} |[[File:7-cube t1.svg|100px]]<BR>Rectified 7-cube<BR>{{CDD|node|4|node_1|3|node|3|node|3|node|3|node|3|node}} ...

...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 ...

|colspan=2|{3^1,7,1}<br>h{4,3⁸}<br>s{2^{1,1,1,1,1,1,1,1,1}} ...]] [[Image:Demiocteract ortho petrie.svg|30px]]<br>5120 [[8-simplex|{3⁷}]] [[Image:8-simplex t0.svg|25px]] ...

These polytopes are part of a family 511 [[uniform 9-polytope]]s with BC₉ symmet |bgcolor=#e7dcc3|[[Schläfli symbol]]|| t₁{3⁷,4} ...

...rtices of a [[6-cube honeycomb]].<ref>Coxeter, '''Regular and Semi-Regular Polytopes III''', (1988), p318</ref> Its facets are [[6-demicube]]s, [[stericated 6-d ** (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 ...

...prism'' exists in some of the [[Uniform 5-polytope#The B5 family|uniform 5-polytopes in the B5 family]]. ...tion of complex polygon, ₃{}×₄{} has 12 vertices and 7 3-edges, shown here with 4 red triangular 3-edges and 3 blue square 4-edges ...

|bgcolor=#e7dcc3|[[Schläfli symbol]]||{3^[7]} = 0_[7] ...dcc3|[[Coxeter notation|Symmetry]]||<math>{\tilde{A}}_6</math>×2, [[3^[7]]] ...

|[[File:7-cube t6.svg|100px]]<BR>[[7-orthoplex]]<BR>{{CDD|node_1|3|node|3|node|3|node|3|node|3|node|4|node}} |[[File:7-cube t5.svg|100px]]<BR>Rectified 7-orthoplex<BR>{{CDD|node|3|node_1|3|node|3|node|3|node|3|node|4|node}} ...