Part of the Atlas of Small Regular Polytopes

Polytope of Type {76,6}

Atlas Canonical Name {76,6}*912b

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(912,207)
Rank
3
Schläfli Type
{76,6}
Vertices, edges, …
76, 228, 6
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 := ( 1, 3)( 2, 4)( 5,75)( 6,76)( 7,73)( 8,74)( 9,71)(10,72)(11,69)(12,70)(13,67)(14,68)(15,65)(16,66)(17,63)(18,64)(19,61)(20,62)(21,59)(22,60)(23,57)(24,58)(25,55)(26,56)(27,53)(28,54)(29,51)(30,52)(31,49)(32,50)(33,47)(34,48)(35,45)(36,46)(37,43)(38,44)(39,41)(40,42);;
s1 := ( 1, 5)( 2, 7)( 3, 6)( 4, 8)( 9,73)(10,75)(11,74)(12,76)(13,69)(14,71)(15,70)(16,72)(17,65)(18,67)(19,66)(20,68)(21,61)(22,63)(23,62)(24,64)(25,57)(26,59)(27,58)(28,60)(29,53)(30,55)(31,54)(32,56)(33,49)(34,51)(35,50)(36,52)(37,45)(38,47)(39,46)(40,48)(42,43);;
s2 := ( 2, 4)( 6, 8)(10,12)(14,16)(18,20)(22,24)(26,28)(30,32)(34,36)(38,40)(42,44)(46,48)(50,52)(54,56)(58,60)(62,64)(66,68)(70,72)(74,76);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*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*s1*s0*s1*s0 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(76)!( 1, 3)( 2, 4)( 5,75)( 6,76)( 7,73)( 8,74)( 9,71)(10,72)(11,69)(12,70)(13,67)(14,68)(15,65)(16,66)(17,63)(18,64)(19,61)(20,62)(21,59)(22,60)(23,57)(24,58)(25,55)(26,56)(27,53)(28,54)(29,51)(30,52)(31,49)(32,50)(33,47)(34,48)(35,45)(36,46)(37,43)(38,44)(39,41)(40,42);
s1 := Sym(76)!( 1, 5)( 2, 7)( 3, 6)( 4, 8)( 9,73)(10,75)(11,74)(12,76)(13,69)(14,71)(15,70)(16,72)(17,65)(18,67)(19,66)(20,68)(21,61)(22,63)(23,62)(24,64)(25,57)(26,59)(27,58)(28,60)(29,53)(30,55)(31,54)(32,56)(33,49)(34,51)(35,50)(36,52)(37,45)(38,47)(39,46)(40,48)(42,43);
s2 := Sym(76)!( 2, 4)( 6, 8)(10,12)(14,16)(18,20)(22,24)(26,28)(30,32)(34,36)(38,40)(42,44)(46,48)(50,52)(54,56)(58,60)(62,64)(66,68)(70,72)(74,76);
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*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*s1*s0*s1*s0 >;

References

None.

to this polytope.

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