Polytope of Type {8,8,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,8,2}*256a
if this polytope has a name.
Group : SmallGroup(256,11462)
Rank : 4
Schlafli Type : {8,8,2}
Number of vertices, edges, etc : 8, 32, 8, 2
Order of s₀s₁s₂s₃ : 8
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {8,8,2,2} of size 512
   {8,8,2,3} of size 768
   {8,8,2,5} of size 1280
   {8,8,2,7} of size 1792
Vertex Figure Of :
   {2,8,8,2} of size 512
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,8,2}*128a, {8,4,2}*128b
   4-fold quotients : {4,4,2}*64, {2,8,2}*64
   8-fold quotients : {2,4,2}*32, {4,2,2}*32
   16-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,8,2}*512a, {8,8,4}*512f, {16,8,2}*512a, {16,8,2}*512b, {8,16,2}*512c, {8,16,2}*512e
   3-fold covers : {8,8,6}*768a, {24,8,2}*768a, {8,24,2}*768b
   5-fold covers : {8,8,10}*1280a, {40,8,2}*1280a, {8,40,2}*1280b
   7-fold covers : {8,8,14}*1792a, {56,8,2}*1792a, {8,56,2}*1792b
Permutation Representation (GAP) :

s0 := ( 1,17)( 2,18)( 3,19)( 4,20)( 5,22)( 6,21)( 7,24)( 8,23)( 9,26)(10,25)
(11,28)(12,27)(13,29)(14,30)(15,31)(16,32)(33,49)(34,50)(35,51)(36,52)(37,54)
(38,53)(39,56)(40,55)(41,58)(42,57)(43,60)(44,59)(45,61)(46,62)(47,63)
(48,64);;
s1 := ( 5, 6)( 7, 8)( 9,11)(10,12)(13,16)(14,15)(17,21)(18,22)(19,23)(20,24)
(25,31)(26,32)(27,29)(28,30)(33,41)(34,42)(35,43)(36,44)(37,46)(38,45)(39,48)
(40,47)(49,62)(50,61)(51,64)(52,63)(53,58)(54,57)(55,60)(56,59);;
s2 := ( 1,33)( 2,34)( 3,35)( 4,36)( 5,38)( 6,37)( 7,40)( 8,39)( 9,43)(10,44)
(11,41)(12,42)(13,48)(14,47)(15,46)(16,45)(17,49)(18,50)(19,51)(20,52)(21,54)
(22,53)(23,56)(24,55)(25,59)(26,60)(27,57)(28,58)(29,64)(30,63)(31,62)
(32,61);;
s3 := (65,66);;
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, 
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(66)!( 1,17)( 2,18)( 3,19)( 4,20)( 5,22)( 6,21)( 7,24)( 8,23)( 9,26)
(10,25)(11,28)(12,27)(13,29)(14,30)(15,31)(16,32)(33,49)(34,50)(35,51)(36,52)
(37,54)(38,53)(39,56)(40,55)(41,58)(42,57)(43,60)(44,59)(45,61)(46,62)(47,63)
(48,64);
s1 := Sym(66)!( 5, 6)( 7, 8)( 9,11)(10,12)(13,16)(14,15)(17,21)(18,22)(19,23)
(20,24)(25,31)(26,32)(27,29)(28,30)(33,41)(34,42)(35,43)(36,44)(37,46)(38,45)
(39,48)(40,47)(49,62)(50,61)(51,64)(52,63)(53,58)(54,57)(55,60)(56,59);
s2 := Sym(66)!( 1,33)( 2,34)( 3,35)( 4,36)( 5,38)( 6,37)( 7,40)( 8,39)( 9,43)
(10,44)(11,41)(12,42)(13,48)(14,47)(15,46)(16,45)(17,49)(18,50)(19,51)(20,52)
(21,54)(22,53)(23,56)(24,55)(25,59)(26,60)(27,57)(28,58)(29,64)(30,63)(31,62)
(32,61);
s3 := Sym(66)!(65,66);
poly := sub<Sym(66)|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, s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope