Polytope of Type {8,2,56}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,2,56}*1792
if this polytope has a name.
Group : SmallGroup(1792,161916)
Rank : 4
Schlafli Type : {8,2,56}
Number of vertices, edges, etc : 8, 8, 56, 56
Order of s₀s₁s₂s₃ : 56
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,2,56}*896, {8,2,28}*896
   4-fold quotients : {4,2,28}*448, {2,2,56}*448, {8,2,14}*448
   7-fold quotients : {8,2,8}*256
   8-fold quotients : {8,2,7}*224, {2,2,28}*224, {4,2,14}*224
   14-fold quotients : {4,2,8}*128, {8,2,4}*128
   16-fold quotients : {4,2,7}*112, {2,2,14}*112
   28-fold quotients : {4,2,4}*64, {2,2,8}*64, {8,2,2}*64
   32-fold quotients : {2,2,7}*56
   56-fold quotients : {2,2,4}*32, {4,2,2}*32
   112-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope