Overview
- Group
- SmallGroup(768,90281)
- Rank
- 3
- Schläfli Type
- {8,12}
- Vertices, edges, …
- 32, 192, 48
- Order of s0s1s2
- 12
- Order of s0s1s2s1
- 8
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
8-fold
12-fold
16-fold
24-fold
32-fold
48-fold
64-fold
96-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
Click an entry to reveal its facets and vertex figures.
Representations
Permutation Representation (GAP)
s0 := ( 1,49)( 2,50)( 3,51)( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)(10,58)(11,59)(12,60)(13,64)(14,65)(15,66)(16,61)(17,62)(18,63)(19,70)(20,71)(21,72)(22,67)(23,68)(24,69)(25,94)(26,95)(27,96)(28,91)(29,92)(30,93)(31,88)(32,89)(33,90)(34,85)(35,86)(36,87)(37,82)(38,83)(39,84)(40,79)(41,80)(42,81)(43,76)(44,77)(45,78)(46,73)(47,74)(48,75);; s1 := ( 2, 3)( 5, 6)( 8, 9)(11,12)(13,19)(14,21)(15,20)(16,22)(17,24)(18,23)(26,27)(29,30)(32,33)(35,36)(37,43)(38,45)(39,44)(40,46)(41,48)(42,47)(49,73)(50,75)(51,74)(52,76)(53,78)(54,77)(55,79)(56,81)(57,80)(58,82)(59,84)(60,83)(61,91)(62,93)(63,92)(64,94)(65,96)(66,95)(67,85)(68,87)(69,86)(70,88)(71,90)(72,89);; s2 := ( 1, 3)( 4, 6)( 7,12)( 8,11)( 9,10)(13,15)(16,18)(19,24)(20,23)(21,22)(25,48)(26,47)(27,46)(28,45)(29,44)(30,43)(31,39)(32,38)(33,37)(34,42)(35,41)(36,40)(49,51)(52,54)(55,60)(56,59)(57,58)(61,63)(64,66)(67,72)(68,71)(69,70)(73,96)(74,95)(75,94)(76,93)(77,92)(78,91)(79,87)(80,86)(81,85)(82,90)(83,89)(84,88);; 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*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
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(96)!( 1,49)( 2,50)( 3,51)( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)(10,58)(11,59)(12,60)(13,64)(14,65)(15,66)(16,61)(17,62)(18,63)(19,70)(20,71)(21,72)(22,67)(23,68)(24,69)(25,94)(26,95)(27,96)(28,91)(29,92)(30,93)(31,88)(32,89)(33,90)(34,85)(35,86)(36,87)(37,82)(38,83)(39,84)(40,79)(41,80)(42,81)(43,76)(44,77)(45,78)(46,73)(47,74)(48,75); s1 := Sym(96)!( 2, 3)( 5, 6)( 8, 9)(11,12)(13,19)(14,21)(15,20)(16,22)(17,24)(18,23)(26,27)(29,30)(32,33)(35,36)(37,43)(38,45)(39,44)(40,46)(41,48)(42,47)(49,73)(50,75)(51,74)(52,76)(53,78)(54,77)(55,79)(56,81)(57,80)(58,82)(59,84)(60,83)(61,91)(62,93)(63,92)(64,94)(65,96)(66,95)(67,85)(68,87)(69,86)(70,88)(71,90)(72,89); s2 := Sym(96)!( 1, 3)( 4, 6)( 7,12)( 8,11)( 9,10)(13,15)(16,18)(19,24)(20,23)(21,22)(25,48)(26,47)(27,46)(28,45)(29,44)(30,43)(31,39)(32,38)(33,37)(34,42)(35,41)(36,40)(49,51)(52,54)(55,60)(56,59)(57,58)(61,63)(64,66)(67,72)(68,71)(69,70)(73,96)(74,95)(75,94)(76,93)(77,92)(78,91)(79,87)(80,86)(81,85)(82,90)(83,89)(84,88); 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*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 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.