Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,76}

Atlas Canonical Name {6,76}*912b

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Overview

Group
SmallGroup(912,207)
Rank
3
Schläfli Type
{6,76}
Vertices, edges, …
6, 228, 76
Order of s0s1s2
57
Order of s0s1s2s1
4
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

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

References

None.

to this polytope.

Twisty Puzzle