Part of the Atlas of Small Regular Polytopes

Polytope of Type {57,6}

Atlas Canonical Name {57,6}*912

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Overview

Group
SmallGroup(912,207)
Rank
3
Schläfli Type
{57,6}
Vertices, edges, …
76, 228, 8
Order of s0s1s2
76
Order of s0s1s2s1
6
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable

Quotients maximal quotients in bold

12-fold

19-fold

38-fold

Covers minimal covers in bold

2-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

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

References

None.

to this polytope.

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