Polytope of Type {4,4,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,2}*64
if this polytope has a name.
Group : SmallGroup(64,202)
Rank : 4
Schlafli Type : {4,4,2}
Number of vertices, edges, etc : 4, 8, 4, 2
Order of s₀s₁s₂s₃ : 4
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,4,2,2} of size 128
   {4,4,2,3} of size 192
   {4,4,2,4} of size 256
   {4,4,2,5} of size 320
   {4,4,2,6} of size 384
   {4,4,2,7} of size 448
   {4,4,2,9} of size 576
   {4,4,2,10} of size 640
   {4,4,2,11} of size 704
   {4,4,2,12} of size 768
   {4,4,2,13} of size 832
   {4,4,2,14} of size 896
   {4,4,2,15} of size 960
   {4,4,2,17} of size 1088
   {4,4,2,18} of size 1152
   {4,4,2,19} of size 1216
   {4,4,2,20} of size 1280
   {4,4,2,21} of size 1344
   {4,4,2,22} of size 1408
   {4,4,2,23} of size 1472
   {4,4,2,25} of size 1600
   {4,4,2,26} of size 1664
   {4,4,2,27} of size 1728
   {4,4,2,28} of size 1792
   {4,4,2,29} of size 1856
   {4,4,2,30} of size 1920
   {4,4,2,31} of size 1984
Vertex Figure Of :
   {2,4,4,2} of size 128
   {4,4,4,2} of size 256
   {6,4,4,2} of size 384
   {3,4,4,2} of size 384
   {8,4,4,2} of size 512
   {8,4,4,2} of size 512
   {4,4,4,2} of size 512
   {6,4,4,2} of size 576
   {10,4,4,2} of size 640
   {12,4,4,2} of size 768
   {6,4,4,2} of size 768
   {14,4,4,2} of size 896
   {5,4,4,2} of size 960
   {18,4,4,2} of size 1152
   {6,4,4,2} of size 1152
   {4,4,4,2} of size 1152
   {9,4,4,2} of size 1152
   {20,4,4,2} of size 1280
   {22,4,4,2} of size 1408
   {10,4,4,2} of size 1600
   {26,4,4,2} of size 1664
   {6,4,4,2} of size 1728
   {28,4,4,2} of size 1792
   {30,4,4,2} of size 1920
   {15,4,4,2} of size 1920
   {5,4,4,2} of size 1920
   {10,4,4,2} of size 1920
   {10,4,4,2} of size 1920
   {6,4,4,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,4,2}*32, {4,2,2}*32
   4-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,4,4}*128, {4,8,2}*128a, {8,4,2}*128a, {4,8,2}*128b, {8,4,2}*128b, {4,4,2}*128
   3-fold covers : {4,12,2}*192a, {12,4,2}*192a, {4,4,6}*192
   4-fold covers : {4,8,2}*256a, {8,4,2}*256a, {8,8,2}*256a, {8,8,2}*256b, {8,8,2}*256c, {8,8,2}*256d, {4,4,8}*256a, {8,4,4}*256a, {4,4,8}*256b, {8,4,4}*256b, {4,8,4}*256a, {4,4,4}*256a, {4,4,4}*256b, {4,8,4}*256b, {4,8,4}*256c, {4,8,4}*256d, {4,16,2}*256a, {16,4,2}*256a, {4,16,2}*256b, {16,4,2}*256b, {4,4,2}*256, {4,8,2}*256b, {8,4,2}*256b
   5-fold covers : {4,20,2}*320, {20,4,2}*320, {4,4,10}*320
   6-fold covers : {4,12,4}*384a, {4,4,12}*384, {12,4,4}*384, {4,24,2}*384a, {24,4,2}*384a, {4,12,2}*384a, {12,4,2}*384a, {4,24,2}*384b, {24,4,2}*384b, {8,12,2}*384a, {12,8,2}*384a, {8,12,2}*384b, {12,8,2}*384b, {4,8,6}*384a, {8,4,6}*384a, {4,8,6}*384b, {8,4,6}*384b, {4,4,6}*384a
   7-fold covers : {4,28,2}*448, {28,4,2}*448, {4,4,14}*448
   8-fold covers : {8,8,2}*512a, {8,4,8}*512a, {8,4,8}*512b, {4,4,4}*512a, {4,8,8}*512a, {8,8,4}*512a, {4,8,8}*512b, {8,8,4}*512b, {4,4,8}*512a, {8,4,4}*512a, {4,8,8}*512c, {8,8,4}*512c, {4,8,8}*512d, {8,8,4}*512d, {4,8,8}*512e, {4,8,8}*512f, {8,8,4}*512e, {8,8,4}*512f, {4,8,8}*512g, {8,8,4}*512g, {4,8,8}*512h, {8,8,4}*512h, {4,4,8}*512b, {8,4,4}*512b, {4,4,8}*512c, {8,4,4}*512c, {4,8,4}*512a, {4,8,4}*512b, {4,8,4}*512c, {4,8,4}*512d, {8,4,8}*512c, {8,4,8}*512d, {4,8,2}*512a, {8,4,2}*512a, {8,8,2}*512b, {8,8,2}*512c, {8,8,2}*512d, {4,16,2}*512a, {16,4,2}*512a, {4,16,2}*512b, {16,4,2}*512b, {8,16,2}*512a, {16,8,2}*512a, {8,16,2}*512b, {16,8,2}*512b, {8,16,2}*512c, {8,16,2}*512d, {16,8,2}*512c, {16,8,2}*512d, {8,16,2}*512e, {8,16,2}*512f, {16,8,2}*512e, {16,8,2}*512f, {4,4,16}*512a, {16,4,4}*512a, {4,4,16}*512b, {16,4,4}*512b, {4,4,4}*512b, {4,4,4}*512c, {4,8,4}*512e, {4,8,4}*512f, {4,8,4}*512g, {4,8,4}*512h, {4,4,8}*512d, {8,4,4}*512d, {4,16,4}*512a, {4,16,4}*512b, {4,16,4}*512c, {4,16,4}*512d, {4,32,2}*512a, {32,4,2}*512a, {4,32,2}*512b, {32,4,2}*512b, {4,4,2}*512, {4,8,2}*512b, {8,4,2}*512b, {4,8,2}*512c, {4,8,2}*512d, {8,4,2}*512c, {8,4,2}*512d, {8,8,2}*512e, {8,8,2}*512f, {8,8,2}*512g, {8,8,2}*512h
   9-fold covers : {4,36,2}*576a, {36,4,2}*576a, {4,4,18}*576, {4,12,6}*576a, {4,12,6}*576b, {12,4,6}*576, {12,12,2}*576a, {12,12,2}*576b, {12,12,2}*576c, {4,12,6}*576c, {4,4,6}*576, {4,4,2}*576, {4,12,2}*576, {12,4,2}*576
   10-fold covers : {4,20,4}*640, {4,4,20}*640, {20,4,4}*640, {4,40,2}*640a, {40,4,2}*640a, {4,20,2}*640, {20,4,2}*640, {4,40,2}*640b, {40,4,2}*640b, {8,20,2}*640a, {20,8,2}*640a, {8,20,2}*640b, {20,8,2}*640b, {4,8,10}*640a, {8,4,10}*640a, {4,8,10}*640b, {8,4,10}*640b, {4,4,10}*640
   11-fold covers : {4,44,2}*704, {44,4,2}*704, {4,4,22}*704
   12-fold covers : {4,8,6}*768a, {8,4,6}*768a, {8,12,2}*768a, {12,8,2}*768a, {4,24,2}*768a, {24,4,2}*768a, {8,8,6}*768a, {8,8,6}*768b, {8,8,6}*768c, {8,24,2}*768a, {24,8,2}*768a, {8,24,2}*768b, {8,24,2}*768c, {24,8,2}*768b, {24,8,2}*768c, {8,8,6}*768d, {8,24,2}*768d, {24,8,2}*768d, {8,4,12}*768a, {12,4,8}*768a, {4,12,8}*768a, {8,12,4}*768a, {4,4,24}*768a, {24,4,4}*768a, {8,4,12}*768b, {12,4,8}*768b, {4,12,8}*768b, {8,12,4}*768b, {4,4,24}*768b, {24,4,4}*768b, {4,8,12}*768a, {12,8,4}*768a, {4,24,4}*768a, {4,4,12}*768a, {12,4,4}*768a, {4,12,4}*768a, {4,12,4}*768b, {4,4,12}*768b, {12,4,4}*768b, {4,8,12}*768b, {12,8,4}*768b, {4,24,4}*768b, {4,24,4}*768c, {4,8,12}*768c, {12,8,4}*768c, {4,8,12}*768d, {12,8,4}*768d, {4,24,4}*768d, {4,16,6}*768a, {16,4,6}*768a, {12,16,2}*768a, {16,12,2}*768a, {4,48,2}*768a, {48,4,2}*768a, {4,16,6}*768b, {16,4,6}*768b, {12,16,2}*768b, {16,12,2}*768b, {4,48,2}*768b, {48,4,2}*768b, {4,4,6}*768a, {4,8,6}*768b, {8,4,6}*768b, {4,12,2}*768a, {4,24,2}*768b, {12,4,2}*768a, {24,4,2}*768b, {8,12,2}*768b, {12,8,2}*768b, {4,12,4}*768e, {4,12,2}*768d, {12,4,2}*768d, {12,12,2}*768a, {4,4,6}*768e, {4,12,6}*768a
   13-fold covers : {4,52,2}*832, {52,4,2}*832, {4,4,26}*832
   14-fold covers : {4,28,4}*896, {4,4,28}*896, {28,4,4}*896, {4,56,2}*896a, {56,4,2}*896a, {4,28,2}*896, {28,4,2}*896, {4,56,2}*896b, {56,4,2}*896b, {8,28,2}*896a, {28,8,2}*896a, {8,28,2}*896b, {28,8,2}*896b, {4,8,14}*896a, {8,4,14}*896a, {4,8,14}*896b, {8,4,14}*896b, {4,4,14}*896
   15-fold covers : {4,12,10}*960a, {12,4,10}*960, {4,20,6}*960, {20,4,6}*960, {12,20,2}*960, {20,12,2}*960, {4,60,2}*960a, {60,4,2}*960a, {4,4,30}*960
   17-fold covers : {4,4,34}*1088, {4,68,2}*1088, {68,4,2}*1088
   18-fold covers : {4,4,36}*1152, {36,4,4}*1152, {4,36,4}*1152a, {4,12,12}*1152a, {4,12,12}*1152b, {12,12,4}*1152a, {12,12,4}*1152b, {4,12,12}*1152c, {12,12,4}*1152c, {12,4,12}*1152, {4,4,4}*1152a, {4,4,4}*1152b, {4,12,4}*1152a, {4,12,4}*1152b, {4,4,12}*1152, {12,4,4}*1152, {4,8,18}*1152a, {8,4,18}*1152a, {8,36,2}*1152a, {36,8,2}*1152a, {4,72,2}*1152a, {72,4,2}*1152a, {8,12,6}*1152a, {8,12,6}*1152b, {12,8,6}*1152a, {4,24,6}*1152a, {8,12,6}*1152c, {4,24,6}*1152b, {4,24,6}*1152c, {24,4,6}*1152a, {12,24,2}*1152a, {12,24,2}*1152b, {24,12,2}*1152a, {24,12,2}*1152b, {12,24,2}*1152c, {24,12,2}*1152c, {8,4,6}*1152a, {4,8,2}*1152a, {4,24,2}*1152a, {8,4,2}*1152a, {24,4,2}*1152a, {8,12,2}*1152a, {12,8,2}*1152a, {4,8,6}*1152a, {4,8,18}*1152b, {8,4,18}*1152b, {8,36,2}*1152b, {36,8,2}*1152b, {4,72,2}*1152b, {72,4,2}*1152b, {8,12,6}*1152d, {8,12,6}*1152e, {12,8,6}*1152b, {4,24,6}*1152d, {8,12,6}*1152f, {4,24,6}*1152e, {4,24,6}*1152f, {24,4,6}*1152b, {12,24,2}*1152d, {12,24,2}*1152e, {24,12,2}*1152d, {24,12,2}*1152e, {12,24,2}*1152f, {24,12,2}*1152f, {4,8,2}*1152b, {4,24,2}*1152b, {8,4,2}*1152b, {24,4,2}*1152b, {8,4,6}*1152b, {8,12,2}*1152b, {12,8,2}*1152b, {4,8,6}*1152b, {4,4,18}*1152a, {4,36,2}*1152a, {36,4,2}*1152a, {4,12,6}*1152a, {4,12,6}*1152b, {12,4,6}*1152a, {4,12,6}*1152c, {12,12,2}*1152a, {12,12,2}*1152b, {12,12,2}*1152c, {4,4,2}*1152, {4,12,2}*1152, {12,4,2}*1152, {4,4,6}*1152a
   19-fold covers : {4,4,38}*1216, {4,76,2}*1216, {76,4,2}*1216
   20-fold covers : {4,8,10}*1280a, {8,4,10}*1280a, {8,20,2}*1280a, {20,8,2}*1280a, {4,40,2}*1280a, {40,4,2}*1280a, {8,8,10}*1280a, {8,8,10}*1280b, {8,8,10}*1280c, {8,40,2}*1280a, {40,8,2}*1280a, {8,40,2}*1280b, {8,40,2}*1280c, {40,8,2}*1280b, {40,8,2}*1280c, {8,8,10}*1280d, {8,40,2}*1280d, {40,8,2}*1280d, {8,4,20}*1280a, {20,4,8}*1280a, {4,20,8}*1280a, {8,20,4}*1280a, {4,4,40}*1280a, {40,4,4}*1280a, {8,4,20}*1280b, {20,4,8}*1280b, {4,20,8}*1280b, {8,20,4}*1280b, {4,4,40}*1280b, {40,4,4}*1280b, {4,8,20}*1280a, {20,8,4}*1280a, {4,40,4}*1280a, {4,4,20}*1280a, {20,4,4}*1280a, {4,20,4}*1280a, {4,20,4}*1280b, {4,4,20}*1280b, {20,4,4}*1280b, {4,8,20}*1280b, {20,8,4}*1280b, {4,40,4}*1280b, {4,40,4}*1280c, {4,8,20}*1280c, {20,8,4}*1280c, {4,8,20}*1280d, {20,8,4}*1280d, {4,40,4}*1280d, {4,16,10}*1280a, {16,4,10}*1280a, {16,20,2}*1280a, {20,16,2}*1280a, {4,80,2}*1280a, {80,4,2}*1280a, {4,16,10}*1280b, {16,4,10}*1280b, {16,20,2}*1280b, {20,16,2}*1280b, {4,80,2}*1280b, {80,4,2}*1280b, {4,4,10}*1280, {4,8,10}*1280b, {8,4,10}*1280b, {4,20,2}*1280a, {4,40,2}*1280b, {20,4,2}*1280a, {40,4,2}*1280b, {8,20,2}*1280b, {20,8,2}*1280b
   21-fold covers : {4,12,14}*1344a, {12,4,14}*1344, {4,28,6}*1344, {28,4,6}*1344, {12,28,2}*1344, {28,12,2}*1344, {4,84,2}*1344a, {84,4,2}*1344a, {4,4,42}*1344
   22-fold covers : {4,4,44}*1408, {44,4,4}*1408, {4,44,4}*1408, {4,8,22}*1408a, {8,4,22}*1408a, {8,44,2}*1408a, {44,8,2}*1408a, {4,88,2}*1408a, {88,4,2}*1408a, {4,8,22}*1408b, {8,4,22}*1408b, {8,44,2}*1408b, {44,8,2}*1408b, {4,88,2}*1408b, {88,4,2}*1408b, {4,4,22}*1408, {4,44,2}*1408, {44,4,2}*1408
   23-fold covers : {4,4,46}*1472, {4,92,2}*1472, {92,4,2}*1472
   25-fold covers : {4,100,2}*1600, {100,4,2}*1600, {4,4,50}*1600, {4,20,10}*1600a, {4,20,10}*1600b, {20,4,10}*1600, {20,20,2}*1600a, {20,20,2}*1600b, {20,20,2}*1600c, {4,20,10}*1600c, {4,4,10}*1600, {4,4,2}*1600, {4,20,2}*1600, {20,4,2}*1600
   26-fold covers : {4,4,52}*1664, {52,4,4}*1664, {4,52,4}*1664, {4,8,26}*1664a, {8,4,26}*1664a, {8,52,2}*1664a, {52,8,2}*1664a, {4,104,2}*1664a, {104,4,2}*1664a, {4,8,26}*1664b, {8,4,26}*1664b, {8,52,2}*1664b, {52,8,2}*1664b, {4,104,2}*1664b, {104,4,2}*1664b, {4,4,26}*1664, {4,52,2}*1664, {52,4,2}*1664
   27-fold covers : {4,108,2}*1728a, {108,4,2}*1728a, {4,4,54}*1728, {4,12,18}*1728a, {12,4,18}*1728, {4,36,6}*1728a, {4,36,6}*1728b, {36,4,6}*1728, {4,12,6}*1728a, {4,12,6}*1728b, {12,12,6}*1728a, {12,36,2}*1728a, {12,36,2}*1728b, {36,12,2}*1728a, {36,12,2}*1728b, {12,12,2}*1728a, {12,12,2}*1728b, {12,12,2}*1728c, {4,12,18}*1728b, {4,12,6}*1728c, {4,4,6}*1728a, {4,12,6}*1728h, {4,12,6}*1728i, {4,12,2}*1728a, {4,12,2}*1728b, {12,4,2}*1728a, {12,4,2}*1728b, {12,12,2}*1728d, {12,12,2}*1728e, {12,12,2}*1728f, {12,12,2}*1728g, {12,12,6}*1728b, {12,12,6}*1728c, {12,12,6}*1728d, {12,12,6}*1728e, {12,12,6}*1728f, {12,12,2}*1728h, {4,12,6}*1728j, {12,12,6}*1728g, {12,4,6}*1728a, {4,12,2}*1728c, {4,12,2}*1728d, {12,4,2}*1728c, {12,4,2}*1728d, {12,12,2}*1728i, {12,12,2}*1728j, {4,4,6}*1728b, {4,4,6}*1728c, {4,12,6}*1728n, {4,12,6}*1728o, {4,12,6}*1728p, {12,4,6}*1728b, {4,12,6}*1728q, {12,12,2}*1728k, {12,12,2}*1728l
   28-fold covers : {4,8,14}*1792a, {8,4,14}*1792a, {8,28,2}*1792a, {28,8,2}*1792a, {4,56,2}*1792a, {56,4,2}*1792a, {8,8,14}*1792a, {8,8,14}*1792b, {8,8,14}*1792c, {8,56,2}*1792a, {56,8,2}*1792a, {8,56,2}*1792b, {8,56,2}*1792c, {56,8,2}*1792b, {56,8,2}*1792c, {8,8,14}*1792d, {8,56,2}*1792d, {56,8,2}*1792d, {8,4,28}*1792a, {28,4,8}*1792a, {4,28,8}*1792a, {8,28,4}*1792a, {4,4,56}*1792a, {56,4,4}*1792a, {8,4,28}*1792b, {28,4,8}*1792b, {4,28,8}*1792b, {8,28,4}*1792b, {4,4,56}*1792b, {56,4,4}*1792b, {4,8,28}*1792a, {28,8,4}*1792a, {4,56,4}*1792a, {4,4,28}*1792a, {28,4,4}*1792a, {4,28,4}*1792a, {4,28,4}*1792b, {4,4,28}*1792b, {28,4,4}*1792b, {4,8,28}*1792b, {28,8,4}*1792b, {4,56,4}*1792b, {4,56,4}*1792c, {4,8,28}*1792c, {28,8,4}*1792c, {4,8,28}*1792d, {28,8,4}*1792d, {4,56,4}*1792d, {4,16,14}*1792a, {16,4,14}*1792a, {16,28,2}*1792a, {28,16,2}*1792a, {4,112,2}*1792a, {112,4,2}*1792a, {4,16,14}*1792b, {16,4,14}*1792b, {16,28,2}*1792b, {28,16,2}*1792b, {4,112,2}*1792b, {112,4,2}*1792b, {4,4,14}*1792, {4,8,14}*1792b, {8,4,14}*1792b, {4,28,2}*1792, {4,56,2}*1792b, {28,4,2}*1792, {56,4,2}*1792b, {8,28,2}*1792b, {28,8,2}*1792b
   29-fold covers : {4,4,58}*1856, {4,116,2}*1856, {116,4,2}*1856
   30-fold covers : {4,4,60}*1920, {60,4,4}*1920, {4,60,4}*1920a, {4,20,12}*1920, {12,20,4}*1920, {4,12,20}*1920a, {20,12,4}*1920a, {12,4,20}*1920, {20,4,12}*1920, {4,8,30}*1920a, {8,4,30}*1920a, {8,60,2}*1920a, {60,8,2}*1920a, {4,120,2}*1920a, {120,4,2}*1920a, {8,12,10}*1920a, {12,8,10}*1920a, {8,20,6}*1920a, {20,8,6}*1920a, {4,24,10}*1920a, {24,4,10}*1920a, {4,40,6}*1920a, {40,4,6}*1920a, {12,40,2}*1920a, {40,12,2}*1920a, {20,24,2}*1920a, {24,20,2}*1920a, {4,8,30}*1920b, {8,4,30}*1920b, {8,60,2}*1920b, {60,8,2}*1920b, {4,120,2}*1920b, {120,4,2}*1920b, {8,12,10}*1920b, {12,8,10}*1920b, {8,20,6}*1920b, {20,8,6}*1920b, {4,24,10}*1920b, {24,4,10}*1920b, {4,40,6}*1920b, {40,4,6}*1920b, {12,40,2}*1920b, {40,12,2}*1920b, {20,24,2}*1920b, {24,20,2}*1920b, {4,4,30}*1920a, {4,60,2}*1920a, {60,4,2}*1920a, {4,12,10}*1920a, {12,4,10}*1920a, {4,20,6}*1920a, {20,4,6}*1920a, {12,20,2}*1920a, {20,12,2}*1920a
   31-fold covers : {4,4,62}*1984, {4,124,2}*1984, {124,4,2}*1984
Permutation Representation (GAP) :

s0 := (2,3)(4,6);;
s1 := (1,2)(3,5)(4,7)(6,8);;
s2 := (2,4)(3,6);;
s3 := ( 9,10);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope