Overview
- Group
- SmallGroup(192,1481)
- Rank
- 3
- Schläfli Type
- {6,12}
- Vertices, edges, …
- 8, 48, 16
- Order of s0s1s2
- 8
- Order of s0s1s2s1
- 12
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
2-fold
4-fold
8-fold
24-fold
Covers minimal covers in bold
2-fold
3-fold
4-fold
5-fold
6-fold
7-fold
9-fold
10-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 3, 5)( 4, 6)( 7, 8)( 9,17)(10,18)(11,21)(12,22)(13,19)(14,20)(15,24)(16,23)(25,26)(27,30)(28,29)(33,42)(34,41)(35,46)(36,45)(37,44)(38,43)(39,47)(40,48)(51,53)(52,54)(55,56)(57,65)(58,66)(59,69)(60,70)(61,67)(62,68)(63,72)(64,71)(73,74)(75,78)(76,77)(81,90)(82,89)(83,94)(84,93)(85,92)(86,91)(87,95)(88,96);; s1 := ( 1,57)( 2,58)( 3,60)( 4,59)( 5,63)( 6,64)( 7,61)( 8,62)( 9,49)(10,50)(11,52)(12,51)(13,55)(14,56)(15,53)(16,54)(17,65)(18,66)(19,68)(20,67)(21,71)(22,72)(23,69)(24,70)(25,82)(26,81)(27,83)(28,84)(29,88)(30,87)(31,86)(32,85)(33,74)(34,73)(35,75)(36,76)(37,80)(38,79)(39,78)(40,77)(41,90)(42,89)(43,91)(44,92)(45,96)(46,95)(47,94)(48,93);; s2 := ( 1,31)( 2,32)( 3,28)( 4,27)( 5,29)( 6,30)( 7,25)( 8,26)( 9,47)(10,48)(11,44)(12,43)(13,45)(14,46)(15,41)(16,42)(17,39)(18,40)(19,36)(20,35)(21,37)(22,38)(23,33)(24,34)(49,79)(50,80)(51,76)(52,75)(53,77)(54,78)(55,73)(56,74)(57,95)(58,96)(59,92)(60,91)(61,93)(62,94)(63,89)(64,90)(65,87)(66,88)(67,84)(68,83)(69,85)(70,86)(71,81)(72,82);; 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*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(96)!( 3, 5)( 4, 6)( 7, 8)( 9,17)(10,18)(11,21)(12,22)(13,19)(14,20)(15,24)(16,23)(25,26)(27,30)(28,29)(33,42)(34,41)(35,46)(36,45)(37,44)(38,43)(39,47)(40,48)(51,53)(52,54)(55,56)(57,65)(58,66)(59,69)(60,70)(61,67)(62,68)(63,72)(64,71)(73,74)(75,78)(76,77)(81,90)(82,89)(83,94)(84,93)(85,92)(86,91)(87,95)(88,96); s1 := Sym(96)!( 1,57)( 2,58)( 3,60)( 4,59)( 5,63)( 6,64)( 7,61)( 8,62)( 9,49)(10,50)(11,52)(12,51)(13,55)(14,56)(15,53)(16,54)(17,65)(18,66)(19,68)(20,67)(21,71)(22,72)(23,69)(24,70)(25,82)(26,81)(27,83)(28,84)(29,88)(30,87)(31,86)(32,85)(33,74)(34,73)(35,75)(36,76)(37,80)(38,79)(39,78)(40,77)(41,90)(42,89)(43,91)(44,92)(45,96)(46,95)(47,94)(48,93); s2 := Sym(96)!( 1,31)( 2,32)( 3,28)( 4,27)( 5,29)( 6,30)( 7,25)( 8,26)( 9,47)(10,48)(11,44)(12,43)(13,45)(14,46)(15,41)(16,42)(17,39)(18,40)(19,36)(20,35)(21,37)(22,38)(23,33)(24,34)(49,79)(50,80)(51,76)(52,75)(53,77)(54,78)(55,73)(56,74)(57,95)(58,96)(59,92)(60,91)(61,93)(62,94)(63,89)(64,90)(65,87)(66,88)(67,84)(68,83)(69,85)(70,86)(71,81)(72,82); poly := sub<Sym(96)|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*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1 >;
References
None.
to this polytope.