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In 6-dimensional geometry, there are 64 uniform polytopes with B6 symmetry. There are two regular forms, the 6-orthoplex, and 6-cube with 12 and 64 vertices respectively. The 6-demicube is added with half the symmetry. They can be visualized as symmetric orthographic projections in Coxeter planes of the B6 Coxeter group, and other subgroups. == Graphs == Symmetric orthographic projections of these 64 polytopes can be made in the B6, B5, B4, B3, B2, A5, A3, Coxeter planes. Ak has ''()'' symmetry, and Bk has ''()'' symmetry. These 64 polytopes are each shown in these 8 symmetry planes, with vertices and edges drawn, and vertices colored by the number of overlapping vertices in each projective position. Rectified 6-orthoplex Rectified hexacontatetrapeton (rag) |- align=center BGCOLOR="#f0e0e0" !3 |80px||80px||80px||80px||80px||80px||80px|| t2 Birectified 6-orthoplex Birectified hexacontatetrapeton (brag) |- align=center BGCOLOR="#e0e0f0" !4 |80px||80px||80px||80px||80px||80px||80px|| t2 Birectified 6-cube Birectified hexeract (brox) |- align=center BGCOLOR="#e0e0f0" !5 |80px||80px||80px||80px||80px||80px||80px|| t1 Rectified 6-cube Rectified hexeract (rax) |- align=center BGCOLOR="#e0e0f0" !6 |80px||80px||80px||80px||80px||80px||80px|| t0 6-cube Hexeract (ax) |- align=center BGCOLOR="#f0e0e0" !7 |80px||80px||80px||80px||80px||80px||80px|| t0,1 Truncated 6-orthoplex Truncated hexacontatetrapeton (tag) |- align=center BGCOLOR="#f0e0e0" !8 |80px||80px||80px||80px||80px||80px||80px|| t0,2 Cantellated 6-orthoplex Small rhombated hexacontatetrapeton (srog) |- align=center BGCOLOR="#f0e0e0" !9 |80px||80px||80px||80px||80px||80px||80px|| t1,2 Bitruncated 6-orthoplex Bitruncated hexacontatetrapeton (botag) |- align=center BGCOLOR="#f0e0e0" !10 |80px||80px||80px||80px||80px||80px||80px|| t0,3 Runcinated 6-orthoplex Small prismated hexacontatetrapeton (spog) |- align=center BGCOLOR="#f0e0e0" !11 |80px||80px||80px||80px||80px||80px||80px|| t1,3 Bicantellated 6-orthoplex Small birhombated hexacontatetrapeton (siborg) |- align=center BGCOLOR="#e0f0e0" !12 |80px||80px||80px||80px||80px||80px||80px|| t2,3 Tritruncated 6-cube Hexeractihexacontitetrapeton (xog) |- align=center BGCOLOR="#f0e0e0" !13 |80px||80px||80px||80px||80px||80px||80px|| t0,4 Stericated 6-orthoplex Small cellated hexacontatetrapeton (scag) |- align=center BGCOLOR="#e0f0e0" !14 |80px||80px||80px||80px||80px||80px||80px|| t1,4 Biruncinated 6-cube Small biprismato-hexeractihexacontitetrapeton (sobpoxog) |- align=center BGCOLOR="#e0e0f0" !15 |80px||80px||80px||80px||80px||80px||80px|| t1,3 Bicantellated 6-cube Small birhombated hexeract (saborx) |- align=center BGCOLOR="#e0e0f0" !16 |80px||80px||80px||80px||80px||80px||80px|| t1,2 Bitruncated 6-cube Bitruncated hexeract (botox) |- align=center BGCOLOR="#e0f0e0" !17 |80px||80px||80px||80px||80px||80px||80px|| t0,5 Pentellated 6-cube Small teri-hexeractihexacontitetrapeton (stoxog) |- align=center BGCOLOR="#e0e0f0" !18 |80px||80px||80px||80px||80px||80px||80px|| t0,4 Stericated 6-cube Small cellated hexeract (scox) |- align=center BGCOLOR="#e0e0f0" !19 |80px||80px||80px||80px||80px||80px||80px|| t0,3 Runcinated 6-cube Small prismated hexeract (spox) |- align=center BGCOLOR="#e0e0f0" !20 |80px||80px||80px||80px||80px||80px||80px|| t0,2 Cantellated 6-cube Small rhombated hexeract (srox) |- align=center BGCOLOR="#e0e0f0" !21 |80px||80px||80px||80px||80px||80px||80px|| t0,1 Truncated 6-cube Truncated hexeract (tox) |- align=center BGCOLOR="#f0e0e0" !22 |80px||80px||80px||80px||80px||80px||80px|| t0,1,2 Cantitruncated 6-orthoplex Great rhombated hexacontatetrapeton (grog) |- align=center BGCOLOR="#f0e0e0" !23 |80px||80px||80px||80px||80px||80px||80px|| t0,1,3 Runcitruncated 6-orthoplex Prismatotruncated hexacontatetrapeton (potag) |- align=center BGCOLOR="#f0e0e0" !24 |80px||80px||80px||80px||80px||80px||80px|| t0,2,3 Runcicantellated 6-orthoplex Prismatorhombated hexacontatetrapeton (prog) |- align=center BGCOLOR="#f0e0e0" !25 |80px||80px||80px||80px||80px||80px||80px|| t1,2,3 Bicantitruncated 6-orthoplex Great birhombated hexacontatetrapeton (gaborg) |- align=center BGCOLOR="#f0e0e0" !26 |80px||80px||80px||80px||80px||80px||80px|| t0,1,4 Steritruncated 6-orthoplex Cellitruncated hexacontatetrapeton (catog) |- align=center BGCOLOR="#f0e0e0" !27 |80px||80px||80px||80px||80px||80px||80px|| t0,2,4 Stericantellated 6-orthoplex Cellirhombated hexacontatetrapeton (crag) |- align=center BGCOLOR="#f0e0e0" !28 |80px||80px||80px||80px||80px||80px||80px|| t1,2,4 Biruncitruncated 6-orthoplex Biprismatotruncated hexacontatetrapeton (boprax) |- align=center BGCOLOR="#f0e0e0" !29 |80px||80px||80px||80px||80px||80px||80px|| t0,3,4 Steriruncinated 6-orthoplex Celliprismated hexacontatetrapeton (copog) |- align=center BGCOLOR="#e0e0f0" !30 |80px||80px||80px||80px||80px||80px||80px|| t1,2,4 Biruncitruncated 6-cube Biprismatotruncated hexeract (boprag) |- align=center BGCOLOR="#e0e0f0" !31 |80px||80px||80px||80px||80px||80px||80px|| t1,2,3 Bicantitruncated 6-cube Great birhombated hexeract (gaborx) |- align=center BGCOLOR="#f0e0e0" !32 |80px||80px||80px||80px||80px||80px||80px|| t0,1,5 Pentitruncated 6-orthoplex Teritruncated hexacontatetrapeton (tacox) |- align=center BGCOLOR="#f0e0e0" !33 |80px||80px||80px||80px||80px||80px||80px|| t0,2,5 Penticantellated 6-orthoplex Terirhombated hexacontatetrapeton (tapox) |- align=center BGCOLOR="#e0e0f0" !34 |80px||80px||80px||80px||80px||80px||80px|| t0,3,4 Steriruncinated 6-cube Celliprismated hexeract (copox) |- align=center BGCOLOR="#e0e0f0" !35 |80px||80px||80px||80px||80px||80px||80px|| t0,2,5 Penticantellated 6-cube Terirhombated hexeract (topag) |- align=center BGCOLOR="#e0e0f0" !36 |80px||80px||80px||80px||80px||80px||80px|| t0,2,4 Stericantellated 6-cube Cellirhombated hexeract (crax) |- align=center BGCOLOR="#e0e0f0" !37 |80px||80px||80px||80px||80px||80px||80px|| t0,2,3 Runcicantellated 6-cube Prismatorhombated hexeract (prox) |- align=center BGCOLOR="#e0e0f0" !38 |80px||80px||80px||80px||80px||80px||80px|| t0,1,5 Pentitruncated 6-cube Teritruncated hexeract (tacog) |- align=center BGCOLOR="#e0e0f0" !39 |80px||80px||80px||80px||80px||80px||80px|| t0,1,4 Steritruncated 6-cube Cellitruncated hexeract (catax) |- align=center BGCOLOR="#e0e0f0" !40 |80px||80px||80px||80px||80px||80px||80px|| t0,1,3 Runcitruncated 6-cube Prismatotruncated hexeract (potax) |- align=center BGCOLOR="#e0e0f0" !41 |80px||80px||80px||80px||80px||80px||80px|| t0,1,2 Cantitruncated 6-cube Great rhombated hexeract (grox) |- align=center BGCOLOR="#f0e0e0" !42 |80px||80px||80px||80px||80px||80px||80px|| t0,1,2,3 Runcicantitruncated 6-orthoplex Great prismated hexacontatetrapeton (gopog) |- align=center BGCOLOR="#f0e0e0" !43 |80px||80px||80px||80px||80px||80px||80px|| t0,1,2,4 Stericantitruncated 6-orthoplex Celligreatorhombated hexacontatetrapeton (cagorg) |- align=center BGCOLOR="#f0e0e0" !44 |80px||80px||80px||80px||80px||80px||80px|| t0,1,3,4 Steriruncitruncated 6-orthoplex Celliprismatotruncated hexacontatetrapeton (captog) |- align=center BGCOLOR="#f0e0e0" !45 |80px||80px||80px||80px||80px||80px||80px|| t0,2,3,4 Steriruncicantellated 6-orthoplex Celliprismatorhombated hexacontatetrapeton (coprag) |- align=center BGCOLOR="#e0f0e0" !46 |80px||80px||80px||80px||80px||80px||80px|| t1,2,3,4 Biruncicantitruncated 6-cube Great biprismato-hexeractihexacontitetrapeton (gobpoxog) |- align=center BGCOLOR="#f0e0e0" !47 |80px||80px||80px||80px||80px||80px||80px|| t0,1,2,5 Penticantitruncated 6-orthoplex Terigreatorhombated hexacontatetrapeton (togrig) |- align=center BGCOLOR="#f0e0e0" !48 |80px||80px||80px||80px||80px||80px||80px|| t0,1,3,5 Pentiruncitruncated 6-orthoplex Teriprismatotruncated hexacontatetrapeton (tocrax) |- align=center BGCOLOR="#e0f0e0" !49 |80px||80px||80px||80px||80px||80px||80px|| t0,2,3,5 Pentiruncicantellated 6-cube Teriprismatorhombi-hexeractihexacontitetrapeton (tiprixog) |- align=center BGCOLOR="#e0e0f0" !50 |80px||80px||80px||80px||80px||80px||80px|| t0,2,3,4 Steriruncicantellated 6-cube Celliprismatorhombated hexeract (coprix) |- align=center BGCOLOR="#e0f0e0" !51 |80px||80px||80px||80px||80px||80px||80px|| t0,1,4,5 Pentisteritruncated 6-cube Tericelli-hexeractihexacontitetrapeton (tactaxog) |- align=center BGCOLOR="#e0e0f0" !52 |80px||80px||80px||80px||80px||80px||80px|| t0,1,3,5 Pentiruncitruncated 6-cube Teriprismatotruncated hexeract (tocrag) |- align=center BGCOLOR="#e0e0f0" !53 |80px||80px||80px||80px||80px||80px||80px|| t0,1,3,4 Steriruncitruncated 6-cube Celliprismatotruncated hexeract (captix) |- align=center BGCOLOR="#e0e0f0" !54 |80px||80px||80px||80px||80px||80px||80px|| t0,1,2,5 Penticantitruncated 6-cube Terigreatorhombated hexeract (togrix) |- align=center BGCOLOR="#e0e0f0" !55 |80px||80px||80px||80px||80px||80px||80px|| t0,1,2,4 Stericantitruncated 6-cube Celligreatorhombated hexeract (cagorx) |- align=center BGCOLOR="#e0e0f0" !56 |80px||80px||80px||80px||80px||80px||80px|| t0,1,2,3 Runcicantitruncated 6-cube Great prismated hexeract (gippox) |- align=center BGCOLOR="#f0e0e0" !57 |80px||80px||80px||80px||80px||80px||80px|| t0,1,2,3,4 Steriruncicantitruncated 6-orthoplex Great cellated hexacontatetrapeton (gocog) |- align=center BGCOLOR="#f0e0e0" !58 |80px||80px||80px||80px||80px||80px||80px|| t0,1,2,3,5 Pentiruncicantitruncated 6-orthoplex Terigreatoprismated hexacontatetrapeton (tagpog) |- align=center BGCOLOR="#f0e0e0" !59 |80px||80px||80px||80px||80px||80px||80px|| t0,1,2,4,5 Pentistericantitruncated 6-orthoplex Tericelligreatorhombated hexacontatetrapeton (tecagorg) |- align=center BGCOLOR="#e0e0f0" !60 |80px||80px||80px||80px||80px||80px||80px|| t0,1,2,4,5 Pentistericantitruncated 6-cube Tericelligreatorhombated hexeract (tocagrax) |- align=center BGCOLOR="#e0e0f0" !61 |80px||80px||80px||80px||80px||80px||80px|| t0,1,2,3,5 Pentiruncicantitruncated 6-cube Terigreatoprismated hexeract (tagpox) |- align=center BGCOLOR="#e0e0f0" !62 |80px||80px||80px||80px||80px||80px||80px|| t0,1,2,3,4 Steriruncicantitruncated 6-cube Great cellated hexeract (gocax) |- align=center BGCOLOR="#e0f0e0" !63 |80px||80px||80px||80px||80px||80px||80px|| t0,1,2,3,4,5 Omnitruncated 6-cube Great teri-hexeractihexacontitetrapeton (gotaxog) |- align=center BGCOLOR="#d0f0f0" !64 || 80px|| 80px||80px|| 80px|| 80px|| 80px|| 80px || h0 6-demicube Hemihexeract |} 抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「List of B6 polytopes」の詳細全文を読む スポンサード リンク
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