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{| class="navbox collapsible"
{| class="wikitable mw-collapsible"
|-
|-
!colspan="13" style="background:lightsteelblue;"|{{tnavbar-collapsible|Fundamental convex [[regular polytope|regular]] and [[uniform polytope]]s in dimensions 2–10 |Polytopes}}
!colspan="13" style="background:lightsteelblue;"|{{navbar-collapsible|Fundamental convex [[regular polytope|regular]] and [[uniform polytope]]s in dimensions 2–10 |Polytopes}}
|- align=center
|- style="text-align:center;"
!class="navbox-group" style="background:gainsboro;"|[[Coxeter_group#Finite_Coxeter_groups|Family]]
!style="background:gainsboro;"|[[Coxeter group#Finite Coxeter groups|Family]]
|style="background:gainsboro;"|[[Simple_Lie_group#A_series|A<sub>n</sub>]]
|style="background:gainsboro;"|[[Simple Lie group#A series|''A''<sub>''n''</sub>]]
|style="background:gainsboro;"|[[Simple_Lie_group#B_series|BC<sub>n</sub>]]
|style="background:gainsboro;"|[[Simple Lie group#B series|''B''<sub>''n''</sub>]]
|style="background:gainsboro;"|[[Simple_Lie_group#D_series|D<sub>n</sub>]]
|style="background:gainsboro;"|{{font color||#f0f0e0|''I''<sub>2</sub>(p)}} / [[Simple Lie group#D series|''D''<sub>''n''</sub>]]
|style="background:gainsboro;"|{{fontcolor||#f0e0e0|[[E6_(mathematics)|E<sub>6</sub>]] / [[E7_(mathematics)|E<sub>7</sub>]] / [[E8_(mathematics)|E<sub>8</sub>]]}} / {{fontcolor||#e0f0e0|[[F4_(mathematics)|F<sub>4</sub>]]}} / {{fontcolor||#e0e0f0|[[G2_(mathematics)|G<sub>2</sub>]]}}
|style="background:gainsboro;"|{{font color||#f0e0e0|[[E6 (mathematics)|''E''<sub>6</sub>]] / [[E7 (mathematics)|''E''<sub>7</sub>]] / [[E8 (mathematics)|''E''<sub>8</sub>]]}} / {{font color||#e0f0e0|[[F4 (mathematics)|''F''<sub>4</sub>]]}} / {{font color||#e0e0f0|[[G2 (mathematics)|''G''<sub>2</sub>]]}}
|style="background:gainsboro;"| [[H4_(mathematics)|H<sub>n</sub>]]
|style="background:gainsboro;"| [[H4 (mathematics)|H<sub>n</sub>]]


|- align=center
|- style="text-align:center;"
!class="navbox-group" style="background:gainsboro;"|[[Regular polygon]]
!style="background:gainsboro;"|[[Regular polygon]]
|[[Triangle]]
|[[Equilateral triangle|Triangle]]
|[[Square (geometry)|Square]]
|[[Square]]
|style="background:#f0f0e0;"|[[regular polygon|p-gon]]
|
|style="background:#e0e0f0;"| [[Hexagon]]
|style="background:#e0e0f0;"| [[Hexagon]]
| [[Pentagon]]
| [[Pentagon]]
|- align=center
|- style="text-align:center;"
!class="navbox-group" style="background:gainsboro;" |[[Uniform polyhedron]]
!style="background:gainsboro;" |[[Uniform polyhedron]]
|style="background:whitesmoke;"|[[Tetrahedron]]
|style="background:whitesmoke;"|[[Tetrahedron]]
|style="background:whitesmoke;"|[[Octahedron]] • [[Cube]]
|style="background:whitesmoke;"|[[Octahedron]] • [[Cube]]
|style="background:whitesmoke;"|[[Tetrahedron|Demicube]]
|style="background:whitesmoke;"|[[Tetrahedron|Demicube]]
|style="background:whitesmoke;"|
|style="background:whitesmoke;"|
|style="background:whitesmoke;"| [[Dodecahedron]] • [[Icosahedron]]
|style="background:whitesmoke;"| [[Regular dodecahedron|Dodecahedron]] • [[Regular icosahedron|Icosahedron]]
|- align=center
|- style="text-align:center;"
!class="navbox-group" style="background:gainsboro;"|[[Uniform polychoron]]
!style="background:gainsboro;"|[[Uniform polychoron]]
|[[5-cell]]
|[[5-cell|Pentachoron]]
|[[16-cell]] • [[Tesseract]]
|[[16-cell]] • [[Tesseract]]
|[[16-cell|Demitesseract]]
|[[16-cell|Demitesseract]]
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| [[120-cell]] • [[600-cell]]
| [[120-cell]] • [[600-cell]]


|- align=center
|- style="text-align:center;"
!class="navbox-group" style="background:gainsboro;"|[[Uniform 5-polytope]]
!style="background:gainsboro;"|[[Uniform 5-polytope]]
|style="background:whitesmoke;"|[[5-simplex]]
|style="background:whitesmoke;"|[[5-simplex]]
|style="background:whitesmoke;"|[[5-orthoplex]] • [[5-cube]]
|style="background:whitesmoke;"|[[5-orthoplex]] • [[5-cube]]
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|style="background:whitesmoke;"|
|style="background:whitesmoke;"|


|- align=center
|- style="text-align:center;"
!class="navbox-group" style="background:gainsboro;"|[[Uniform 6-polytope]]
!style="background:gainsboro;"|[[Uniform 6-polytope]]
|[[6-simplex]]
|[[6-simplex]]
|[[6-orthoplex]] • [[6-cube]]
|[[6-orthoplex]] • [[6-cube]]
|[[6-demicube]]
|[[6-demicube]]
|style="background:#f0e0e0;"| [[1_22 polytope|1<sub>22</sub>]] • [[2_21 polytope|2<sub>21</sub>]]
|style="background:#f0e0e0;"| [[1 22 polytope|1<sub>22</sub>]] • [[2 21 polytope|2<sub>21</sub>]]
|
|


|- align=center
|- style="text-align:center;"
!class="navbox-group" style="background:gainsboro;"|[[Uniform 7-polytope]]
!style="background:gainsboro;"|[[Uniform 7-polytope]]
|style="background:whitesmoke;"|[[7-simplex]]
|style="background:whitesmoke;"|[[7-simplex]]
|style="background:whitesmoke;"|[[7-orthoplex]] • [[7-cube]]
|style="background:whitesmoke;"|[[7-orthoplex]] • [[7-cube]]
|style="background:whitesmoke;"|[[7-demicube]]
|style="background:whitesmoke;"|[[7-demicube]]
|style="background:#f0e0e0;"| [[1_32 polytope|1<sub>32</sub>]] • [[2_31 polytope|2<sub>31</sub>]] • [[3_21 polytope|3<sub>21</sub>]]
|style="background:#f0e0e0;"| [[1 32 polytope|1<sub>32</sub>]] • [[2 31 polytope|2<sub>31</sub>]] • [[3 21 polytope|3<sub>21</sub>]]
|style="background:whitesmoke;"|
|style="background:whitesmoke;"|


|- align=center
|- style="text-align:center;"
!class="navbox-group" style="background:gainsboro;"|[[Uniform 8-polytope]]
!style="background:gainsboro;"|[[Uniform 8-polytope]]
|[[8-simplex]]
|[[8-simplex]]
|[[8-orthoplex]] • [[8-cube]]
|[[8-orthoplex]] • [[8-cube]]
|[[8-demicube]]
|[[8-demicube]]
|style="background:#f0e0e0;"| [[1_42 polytope|1<sub>42</sub>]] • [[2_41 polytope|2<sub>41</sub>]] • [[4_21 polytope|4<sub>21</sub>]]
|style="background:#f0e0e0;"| [[1 42 polytope|1<sub>42</sub>]] • [[2 41 polytope|2<sub>41</sub>]] • [[4 21 polytope|4<sub>21</sub>]]
|
|


|- align=center
|- style="text-align:center;"
!class="navbox-group" style="background:gainsboro;"|[[Uniform 9-polytope]]
!style="background:gainsboro;"|[[Uniform 9-polytope]]
|style="background:whitesmoke;"|[[9-simplex]]
|style="background:whitesmoke;"|[[9-simplex]]
|style="background:whitesmoke;"|[[9-orthoplex]] • [[9-cube]]
|style="background:whitesmoke;"|[[9-orthoplex]] • [[9-cube]]
|style="background:whitesmoke;"|[[9-demicube]]
|style="background:whitesmoke;"|[[9-demicube]]
|style="background:whitesmoke;"|
|style="background:whitesmoke;"|
|style="background:whitesmoke;"|
|style="background:whitesmoke;"|


|- align=center
|- style="text-align:center;"
!class="navbox-group" style="background:gainsboro;"|[[Uniform 10-polytope]]
!style="background:gainsboro;"|[[Uniform 10-polytope]]
|[[10-simplex]]
|[[10-simplex]]
|[[10-orthoplex]] • [[10-cube]]
|[[10-orthoplex]] • [[10-cube]]
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|
|


|- align=center
|- style="text-align:center;"
!class="navbox-group" style="background:gainsboro;"|Uniform ''n''-[[polytope]]
!style="background:gainsboro;"|Uniform ''n''-[[polytope]]
|style="background:whitesmoke;"|''n''-[[simplex]]
|style="background:whitesmoke;"|''n''-[[simplex]]
|style="background:whitesmoke;"|''n''-[[orthoplex]] • ''n''-[[hypercube|cube]]
|style="background:whitesmoke;"|''n''-[[Cross-polytope|orthoplex]] • ''n''-[[hypercube|cube]]
|style="background:whitesmoke;"|''n''-[[demihypercube|demicube]]
|style="background:whitesmoke;"|''n''-[[demihypercube|demicube]]
|style="background:#f0e0e0;"|[[Uniform 1 k2 polytope|1<sub>k2</sub>]] • [[Uniform 2 k1 polytope|2<sub>k1</sub>]] • [[Uniform k 21 polytope|k<sub>21</sub>]]
|style="background:#f0e0e0;"|[[Uniform 1 k2 polytope|1<sub>k2</sub>]] • [[Uniform 2 k1 polytope|2<sub>k1</sub>]] • [[Uniform k 21 polytope|k<sub>21</sub>]]
|style="background:whitesmoke;"|''n''-[[pentagonal polytope]]
|style="background:whitesmoke;"|''n''-[[pentagonal polytope]]


|- align=center
|- style="text-align:center;"
!colspan="13" style="background:gainsboro;"|Topics: [[Polytope families]] • [[Regular polytope]] • [[List of regular polytopes]]
!colspan="13" style="background:gainsboro;"|Topics: [[Polytope families]] • [[Regular polytope]] • [[List of regular polytopes and compounds]]
|}<noinclude>[[Category:Polytopes]]
|}<noinclude>{{documentation|content=
==See also==

*{{tl|Honeycombs}}
[[Category:Mathematics templates|{{PAGENAME}}]]</noinclude>
[[Category:Polytopes]]
[[Category:Geometry navigational boxes]]
}}</noinclude>

Latest revision as of 20:24, 3 April 2024

Fundamental convex regular and uniform polytopes in dimensions 2–10
Family An Bn I2(p) / Dn E6 / E7 / E8 / F4 / G2 Hn
Regular polygon Triangle Square p-gon Hexagon Pentagon
Uniform polyhedron Tetrahedron Octahedron • Cube Demicube Dodecahedron • Icosahedron
Uniform polychoron Pentachoron 16-cell • Tesseract Demitesseract 24-cell 120-cell • 600-cell
Uniform 5-polytope 5-simplex 5-orthoplex • 5-cube 5-demicube
Uniform 6-polytope 6-simplex 6-orthoplex • 6-cube 6-demicube 122 • 221
Uniform 7-polytope 7-simplex 7-orthoplex • 7-cube 7-demicube 132 • 231 • 321
Uniform 8-polytope 8-simplex 8-orthoplex • 8-cube 8-demicube 142 • 241 • 421
Uniform 9-polytope 9-simplex 9-orthoplex • 9-cube 9-demicube
Uniform 10-polytope 10-simplex 10-orthoplex • 10-cube 10-demicube
Uniform n-polytope n-simplex n-orthoplex • n-cube n-demicube 1k2 • 2k1 • k21 n-pentagonal polytope
Topics: Polytope families • Regular polytope • List of regular polytopes and compounds
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