Overview
- Group
- SmallGroup(768,90280)
- Rank
- 3
- Schläfli Type
- {24,4}
- Vertices, edges, …
- 96, 192, 16
- 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)( 2,51)( 3,50)( 4,52)( 5,54)( 6,53)( 7,55)( 8,57)( 9,56)(10,58)(11,60)(12,59)(13,64)(14,66)(15,65)(16,61)(17,63)(18,62)(19,70)(20,72)(21,71)(22,67)(23,69)(24,68)(25,94)(26,96)(27,95)(28,91)(29,93)(30,92)(31,88)(32,90)(33,89)(34,85)(35,87)(36,86)(37,82)(38,84)(39,83)(40,79)(41,81)(42,80)(43,76)(44,78)(45,77)(46,73)(47,75)(48,74);; s1 := ( 1, 3)( 4, 6)( 7, 9)(10,12)(13,21)(14,20)(15,19)(16,24)(17,23)(18,22)(25,27)(28,30)(31,33)(34,36)(37,45)(38,44)(39,43)(40,48)(41,47)(42,46)(49,75)(50,74)(51,73)(52,78)(53,77)(54,76)(55,81)(56,80)(57,79)(58,84)(59,83)(60,82)(61,93)(62,92)(63,91)(64,96)(65,95)(66,94)(67,87)(68,86)(69,85)(70,90)(71,89)(72,88);; s2 := ( 7,10)( 8,11)( 9,12)(19,22)(20,23)(21,24)(25,46)(26,47)(27,48)(28,43)(29,44)(30,45)(31,37)(32,38)(33,39)(34,40)(35,41)(36,42)(55,58)(56,59)(57,60)(67,70)(68,71)(69,72)(73,94)(74,95)(75,96)(76,91)(77,92)(78,93)(79,85)(80,86)(81,87)(82,88)(83,89)(84,90);; 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,
s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1,
s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(96)!( 1,49)( 2,51)( 3,50)( 4,52)( 5,54)( 6,53)( 7,55)( 8,57)( 9,56)(10,58)(11,60)(12,59)(13,64)(14,66)(15,65)(16,61)(17,63)(18,62)(19,70)(20,72)(21,71)(22,67)(23,69)(24,68)(25,94)(26,96)(27,95)(28,91)(29,93)(30,92)(31,88)(32,90)(33,89)(34,85)(35,87)(36,86)(37,82)(38,84)(39,83)(40,79)(41,81)(42,80)(43,76)(44,78)(45,77)(46,73)(47,75)(48,74); s1 := Sym(96)!( 1, 3)( 4, 6)( 7, 9)(10,12)(13,21)(14,20)(15,19)(16,24)(17,23)(18,22)(25,27)(28,30)(31,33)(34,36)(37,45)(38,44)(39,43)(40,48)(41,47)(42,46)(49,75)(50,74)(51,73)(52,78)(53,77)(54,76)(55,81)(56,80)(57,79)(58,84)(59,83)(60,82)(61,93)(62,92)(63,91)(64,96)(65,95)(66,94)(67,87)(68,86)(69,85)(70,90)(71,89)(72,88); s2 := Sym(96)!( 7,10)( 8,11)( 9,12)(19,22)(20,23)(21,24)(25,46)(26,47)(27,48)(28,43)(29,44)(30,45)(31,37)(32,38)(33,39)(34,40)(35,41)(36,42)(55,58)(56,59)(57,60)(67,70)(68,71)(69,72)(73,94)(74,95)(75,96)(76,91)(77,92)(78,93)(79,85)(80,86)(81,87)(82,88)(83,89)(84,90); 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, s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1, s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0 >;
References
None.
to this polytope.