Polytope of Type {2,8,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,2}*64
if this polytope has a name.
Group : SmallGroup(64,250)
Rank : 4
Schlafli Type : {2,8,2}
Number of vertices, edges, etc : 2, 8, 8, 2
Order of s₀s₁s₂s₃ : 8
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,8,2,2} of size 128
   {2,8,2,3} of size 192
   {2,8,2,4} of size 256
   {2,8,2,5} of size 320
   {2,8,2,6} of size 384
   {2,8,2,7} of size 448
   {2,8,2,8} of size 512
   {2,8,2,9} of size 576
   {2,8,2,10} of size 640
   {2,8,2,11} of size 704
   {2,8,2,12} of size 768
   {2,8,2,13} of size 832
   {2,8,2,14} of size 896
   {2,8,2,15} of size 960
   {2,8,2,17} of size 1088
   {2,8,2,18} of size 1152
   {2,8,2,19} of size 1216
   {2,8,2,20} of size 1280
   {2,8,2,21} of size 1344
   {2,8,2,22} of size 1408
   {2,8,2,23} of size 1472
   {2,8,2,25} of size 1600
   {2,8,2,26} of size 1664
   {2,8,2,27} of size 1728
   {2,8,2,28} of size 1792
   {2,8,2,29} of size 1856
   {2,8,2,30} of size 1920
   {2,8,2,31} of size 1984
Vertex Figure Of :
   {2,2,8,2} of size 128
   {3,2,8,2} of size 192
   {4,2,8,2} of size 256
   {5,2,8,2} of size 320
   {6,2,8,2} of size 384
   {7,2,8,2} of size 448
   {8,2,8,2} of size 512
   {9,2,8,2} of size 576
   {10,2,8,2} of size 640
   {11,2,8,2} of size 704
   {12,2,8,2} of size 768
   {13,2,8,2} of size 832
   {14,2,8,2} of size 896
   {15,2,8,2} of size 960
   {17,2,8,2} of size 1088
   {18,2,8,2} of size 1152
   {19,2,8,2} of size 1216
   {20,2,8,2} of size 1280
   {21,2,8,2} of size 1344
   {22,2,8,2} of size 1408
   {23,2,8,2} of size 1472
   {25,2,8,2} of size 1600
   {26,2,8,2} of size 1664
   {27,2,8,2} of size 1728
   {28,2,8,2} of size 1792
   {29,2,8,2} of size 1856
   {30,2,8,2} of size 1920
   {31,2,8,2} of size 1984
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,4,2}*32
   4-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,8,4}*128a, {4,8,2}*128a, {2,16,2}*128
   3-fold covers : {2,24,2}*192, {2,8,6}*192, {6,8,2}*192
   4-fold covers : {2,8,4}*256a, {4,8,2}*256a, {2,8,8}*256b, {2,8,8}*256c, {8,8,2}*256a, {8,8,2}*256b, {4,8,4}*256d, {2,16,4}*256a, {4,16,2}*256a, {2,16,4}*256b, {4,16,2}*256b, {2,32,2}*256
   5-fold covers : {2,40,2}*320, {2,8,10}*320, {10,8,2}*320
   6-fold covers : {2,24,4}*384a, {4,24,2}*384a, {2,8,12}*384a, {12,8,2}*384a, {4,8,6}*384a, {6,8,4}*384a, {2,48,2}*384, {2,16,6}*384, {6,16,2}*384
   7-fold covers : {2,56,2}*448, {2,8,14}*448, {14,8,2}*448
   8-fold covers : {2,8,8}*512a, {8,8,2}*512a, {4,8,8}*512e, {4,8,8}*512f, {8,8,4}*512e, {8,8,4}*512f, {4,8,4}*512a, {4,8,4}*512b, {2,8,4}*512a, {4,8,2}*512a, {2,8,8}*512d, {8,8,2}*512c, {2,16,4}*512a, {4,16,2}*512a, {2,16,4}*512b, {4,16,2}*512b, {2,8,16}*512a, {16,8,2}*512a, {2,8,16}*512b, {16,8,2}*512b, {2,8,16}*512d, {2,16,8}*512c, {2,16,8}*512d, {8,16,2}*512c, {8,16,2}*512d, {16,8,2}*512d, {2,8,16}*512f, {2,16,8}*512e, {2,16,8}*512f, {8,16,2}*512e, {8,16,2}*512f, {16,8,2}*512f, {4,16,4}*512a, {4,16,4}*512b, {4,16,4}*512c, {4,16,4}*512d, {2,32,4}*512a, {4,32,2}*512a, {2,32,4}*512b, {4,32,2}*512b, {2,64,2}*512
   9-fold covers : {2,72,2}*576, {2,8,18}*576, {18,8,2}*576, {2,24,6}*576a, {2,24,6}*576b, {6,24,2}*576a, {6,24,2}*576b, {6,8,6}*576, {2,24,6}*576c, {6,24,2}*576c, {2,8,6}*576, {6,8,2}*576
   10-fold covers : {2,40,4}*640a, {4,40,2}*640a, {2,8,20}*640a, {20,8,2}*640a, {4,8,10}*640a, {10,8,4}*640a, {2,80,2}*640, {2,16,10}*640, {10,16,2}*640
   11-fold covers : {2,88,2}*704, {2,8,22}*704, {22,8,2}*704
   12-fold covers : {4,8,6}*768a, {6,8,4}*768a, {2,8,12}*768a, {12,8,2}*768a, {2,24,4}*768a, {4,24,2}*768a, {6,8,8}*768b, {6,8,8}*768c, {8,8,6}*768a, {8,8,6}*768b, {2,8,24}*768a, {24,8,2}*768a, {2,8,24}*768c, {2,24,8}*768b, {2,24,8}*768c, {8,24,2}*768b, {8,24,2}*768c, {24,8,2}*768c, {4,8,12}*768d, {12,8,4}*768d, {4,24,4}*768d, {4,16,6}*768a, {6,16,4}*768a, {2,16,12}*768a, {12,16,2}*768a, {2,48,4}*768a, {4,48,2}*768a, {4,16,6}*768b, {6,16,4}*768b, {2,16,12}*768b, {12,16,2}*768b, {2,48,4}*768b, {4,48,2}*768b, {2,32,6}*768, {6,32,2}*768, {2,96,2}*768, {2,24,4}*768c, {4,24,2}*768c, {2,8,6}*768g, {2,24,6}*768a, {6,8,2}*768g, {6,24,2}*768a
   13-fold covers : {2,104,2}*832, {2,8,26}*832, {26,8,2}*832
   14-fold covers : {2,56,4}*896a, {4,56,2}*896a, {2,8,28}*896a, {28,8,2}*896a, {4,8,14}*896a, {14,8,4}*896a, {2,112,2}*896, {2,16,14}*896, {14,16,2}*896
   15-fold covers : {2,24,10}*960, {10,24,2}*960, {2,40,6}*960, {6,40,2}*960, {6,8,10}*960, {10,8,6}*960, {2,120,2}*960, {2,8,30}*960, {30,8,2}*960
   17-fold covers : {2,8,34}*1088, {34,8,2}*1088, {2,136,2}*1088
   18-fold covers : {4,8,18}*1152a, {18,8,4}*1152a, {2,8,36}*1152a, {36,8,2}*1152a, {2,72,4}*1152a, {4,72,2}*1152a, {6,8,12}*1152a, {12,8,6}*1152a, {4,24,6}*1152a, {6,24,4}*1152a, {4,24,6}*1152b, {4,24,6}*1152c, {6,24,4}*1152b, {6,24,4}*1152c, {2,24,12}*1152a, {2,24,12}*1152b, {12,24,2}*1152a, {12,24,2}*1152b, {2,24,12}*1152c, {12,24,2}*1152c, {2,8,4}*1152a, {2,24,4}*1152a, {4,8,2}*1152a, {4,24,2}*1152a, {2,8,12}*1152a, {12,8,2}*1152a, {4,8,6}*1152a, {6,8,4}*1152a, {2,16,18}*1152, {18,16,2}*1152, {2,144,2}*1152, {6,16,6}*1152, {2,48,6}*1152a, {6,48,2}*1152a, {2,48,6}*1152b, {2,48,6}*1152c, {6,48,2}*1152b, {6,48,2}*1152c, {2,16,6}*1152, {6,16,2}*1152
   19-fold covers : {2,8,38}*1216, {38,8,2}*1216, {2,152,2}*1216
   20-fold covers : {4,8,10}*1280a, {10,8,4}*1280a, {2,8,20}*1280a, {20,8,2}*1280a, {2,40,4}*1280a, {4,40,2}*1280a, {8,8,10}*1280a, {8,8,10}*1280b, {10,8,8}*1280b, {10,8,8}*1280c, {2,8,40}*1280a, {40,8,2}*1280a, {2,8,40}*1280c, {2,40,8}*1280b, {2,40,8}*1280c, {8,40,2}*1280b, {8,40,2}*1280c, {40,8,2}*1280c, {4,8,20}*1280d, {20,8,4}*1280d, {4,40,4}*1280d, {4,16,10}*1280a, {10,16,4}*1280a, {2,16,20}*1280a, {20,16,2}*1280a, {2,80,4}*1280a, {4,80,2}*1280a, {4,16,10}*1280b, {10,16,4}*1280b, {2,16,20}*1280b, {20,16,2}*1280b, {2,80,4}*1280b, {4,80,2}*1280b, {2,32,10}*1280, {10,32,2}*1280, {2,160,2}*1280
   21-fold covers : {2,24,14}*1344, {14,24,2}*1344, {2,56,6}*1344, {6,56,2}*1344, {6,8,14}*1344, {14,8,6}*1344, {2,168,2}*1344, {2,8,42}*1344, {42,8,2}*1344
   22-fold covers : {4,8,22}*1408a, {22,8,4}*1408a, {2,8,44}*1408a, {44,8,2}*1408a, {2,88,4}*1408a, {4,88,2}*1408a, {2,16,22}*1408, {22,16,2}*1408, {2,176,2}*1408
   23-fold covers : {2,8,46}*1472, {46,8,2}*1472, {2,184,2}*1472
   25-fold covers : {2,200,2}*1600, {2,8,50}*1600, {50,8,2}*1600, {2,40,10}*1600a, {2,40,10}*1600b, {10,40,2}*1600a, {10,40,2}*1600b, {10,8,10}*1600, {2,40,10}*1600c, {10,40,2}*1600c, {2,8,10}*1600, {10,8,2}*1600
   26-fold covers : {4,8,26}*1664a, {26,8,4}*1664a, {2,8,52}*1664a, {52,8,2}*1664a, {2,104,4}*1664a, {4,104,2}*1664a, {2,16,26}*1664, {26,16,2}*1664, {2,208,2}*1664
   27-fold covers : {2,216,2}*1728, {2,8,54}*1728, {54,8,2}*1728, {2,72,6}*1728a, {2,72,6}*1728b, {6,72,2}*1728a, {6,72,2}*1728b, {2,24,18}*1728a, {18,24,2}*1728a, {2,24,6}*1728a, {2,24,6}*1728b, {6,24,2}*1728a, {6,24,2}*1728b, {6,8,18}*1728, {18,8,6}*1728, {6,24,6}*1728a, {2,24,18}*1728b, {18,24,2}*1728b, {2,24,6}*1728c, {6,24,2}*1728c, {2,8,6}*1728a, {2,24,6}*1728d, {2,24,6}*1728e, {6,8,2}*1728a, {6,24,2}*1728d, {6,24,2}*1728e, {6,24,6}*1728b, {6,24,6}*1728c, {6,24,6}*1728d, {6,24,6}*1728e, {2,24,6}*1728f, {6,24,2}*1728f, {6,24,6}*1728f, {6,24,6}*1728g, {6,8,6}*1728a, {6,8,6}*1728b, {2,8,6}*1728b, {2,24,6}*1728g, {6,8,2}*1728b, {6,24,2}*1728g, {2,24,6}*1728h, {6,24,2}*1728h
   28-fold covers : {4,8,14}*1792a, {14,8,4}*1792a, {2,8,28}*1792a, {28,8,2}*1792a, {2,56,4}*1792a, {4,56,2}*1792a, {8,8,14}*1792a, {8,8,14}*1792b, {14,8,8}*1792b, {14,8,8}*1792c, {2,8,56}*1792a, {56,8,2}*1792a, {2,8,56}*1792c, {2,56,8}*1792b, {2,56,8}*1792c, {8,56,2}*1792b, {8,56,2}*1792c, {56,8,2}*1792c, {4,8,28}*1792d, {28,8,4}*1792d, {4,56,4}*1792d, {4,16,14}*1792a, {14,16,4}*1792a, {2,16,28}*1792a, {28,16,2}*1792a, {2,112,4}*1792a, {4,112,2}*1792a, {4,16,14}*1792b, {14,16,4}*1792b, {2,16,28}*1792b, {28,16,2}*1792b, {2,112,4}*1792b, {4,112,2}*1792b, {2,32,14}*1792, {14,32,2}*1792, {2,224,2}*1792
   29-fold covers : {2,8,58}*1856, {58,8,2}*1856, {2,232,2}*1856
   30-fold covers : {4,8,30}*1920a, {30,8,4}*1920a, {2,8,60}*1920a, {60,8,2}*1920a, {2,120,4}*1920a, {4,120,2}*1920a, {10,8,12}*1920a, {12,8,10}*1920a, {6,8,20}*1920a, {20,8,6}*1920a, {4,24,10}*1920a, {10,24,4}*1920a, {4,40,6}*1920a, {6,40,4}*1920a, {2,40,12}*1920a, {12,40,2}*1920a, {2,24,20}*1920a, {20,24,2}*1920a, {2,16,30}*1920, {30,16,2}*1920, {2,240,2}*1920, {6,16,10}*1920, {10,16,6}*1920, {2,48,10}*1920, {10,48,2}*1920, {2,80,6}*1920, {6,80,2}*1920
   31-fold covers : {2,8,62}*1984, {62,8,2}*1984, {2,248,2}*1984
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (4,5)(6,7)(8,9);;
s2 := ( 3, 4)( 5, 6)( 7, 8)( 9,10);;
s3 := (11,12);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(12)!(1,2);
s1 := Sym(12)!(4,5)(6,7)(8,9);
s2 := Sym(12)!( 3, 4)( 5, 6)( 7, 8)( 9,10);
s3 := Sym(12)!(11,12);
poly := sub<Sym(12)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope