Overview
- Group
- SmallGroup(912,207)
- Rank
- 3
- Schläfli Type
- {6,57}
- Vertices, edges, …
- 8, 228, 76
- 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)( 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.