Polytope of Type {6,57}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,57}*912
if this polytope has a name.
Group : SmallGroup(912,207)
Rank : 3
Schlafli Type : {6,57}
Number of vertices, edges, etc : 8, 228, 76
Order of s₀s₁s₂ : 76
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,57,2} of size 1824
Vertex Figure Of :
   {2,6,57} of size 1824
Quotients (Maximal Quotients in Boldface) :
   12-fold quotients : {2,19}*76
   19-fold quotients : {6,3}*48
   38-fold quotients : {3,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,57}*1824, {6,114}*1824
Irregular Quotients (of which this is a minimal cover):
   None.

Permutation Representation (GAP) :

s0 := ( 2, 3)( 6, 7)(10,11)(14,15)(18,19)(22,23)(26,27)(30,31)(34,35)(38,39)(42,43)(46,47)(50,51)(54,55)(58,59)(62,63)(66,67)(70,71)(74,75);;
s1 := ( 3, 4)( 5,73)( 6,74)( 7,76)( 8,75)( 9,69)(10,70)(11,72)(12,71)(13,65)(14,66)(15,68)(16,67)(17,61)(18,62)(19,64)(20,63)(21,57)(22,58)(23,60)(24,59)(25,53)(26,54)(27,56)(28,55)(29,49)(30,50)(31,52)(32,51)(33,45)(34,46)(35,48)(36,47)(37,41)(38,42)(39,44)(40,43);;
s2 := ( 1, 8)( 2, 6)( 3, 7)( 4, 5)( 9,76)(10,74)(11,75)(12,73)(13,72)(14,70)(15,71)(16,69)(17,68)(18,66)(19,67)(20,65)(21,64)(22,62)(23,63)(24,61)(25,60)(26,58)(27,59)(28,57)(29,56)(30,54)(31,55)(32,53)(33,52)(34,50)(35,51)(36,49)(37,48)(38,46)(39,47)(40,45)(41,44);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

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

Permutation Representation (Magma) :

s0 := Sym(76)!( 2, 3)( 6, 7)(10,11)(14,15)(18,19)(22,23)(26,27)(30,31)(34,35)(38,39)(42,43)(46,47)(50,51)(54,55)(58,59)(62,63)(66,67)(70,71)(74,75);
s1 := Sym(76)!( 3, 4)( 5,73)( 6,74)( 7,76)( 8,75)( 9,69)(10,70)(11,72)(12,71)(13,65)(14,66)(15,68)(16,67)(17,61)(18,62)(19,64)(20,63)(21,57)(22,58)(23,60)(24,59)(25,53)(26,54)(27,56)(28,55)(29,49)(30,50)(31,52)(32,51)(33,45)(34,46)(35,48)(36,47)(37,41)(38,42)(39,44)(40,43);
s2 := Sym(76)!( 1, 8)( 2, 6)( 3, 7)( 4, 5)( 9,76)(10,74)(11,75)(12,73)(13,72)(14,70)(15,71)(16,69)(17,68)(18,66)(19,67)(20,65)(21,64)(22,62)(23,63)(24,61)(25,60)(26,58)(27,59)(28,57)(29,56)(30,54)(31,55)(32,53)(33,52)(34,50)(35,51)(36,49)(37,48)(38,46)(39,47)(40,45)(41,44);
poly := sub<Sym(76)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {6,57}

Twisty Puzzle