Overview
- Group
- SmallGroup(384,17949)
- Rank
- 3
- Schläfli Type
- {8,6}
- Vertices, edges, …
- 32, 96, 24
- Order of s0s1s2
- 6
- 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
4-fold
8-fold
16-fold
32-fold
48-fold
Covers minimal covers in bold
2-fold
3-fold
5-fold
Irregular Quotients of which this is a minimal cover
Click an entry to reveal its facets and vertex figures.
P/N, where N=<s0*s1*s2*(s1*s0)^2*s2*s1> of order 2
12 facets
- 12 of {8}*16
16 vertex figures
- 16 of {6}*12
P/N, where N=<(s0*s1)^4, s0*s1*s2*(s1*s0)^3*s2*s1*s2> of order 4
8 facets
8 vertex figures
- 8 of {6}*12
P/N, where N=<(s0*s1)^4, s0*s1*s2*(s1*s0)^3*s1*s2*s1> of order 4
8 facets
8 vertex figures
- 8 of {6}*12
Representations
Permutation Representation (GAP)
s0 := ( 1, 9)( 2,10)( 3,11)( 4,12)( 5,16)( 6,15)( 7,14)( 8,13)(17,25)(18,26)(19,27)(20,28)(21,32)(22,31)(23,30)(24,29)(33,41)(34,42)(35,43)(36,44)(37,48)(38,47)(39,46)(40,45)(49,57)(50,58)(51,59)(52,60)(53,64)(54,63)(55,62)(56,61)(65,73)(66,74)(67,75)(68,76)(69,80)(70,79)(71,78)(72,77)(81,89)(82,90)(83,91)(84,92)(85,96)(86,95)(87,94)(88,93);; s1 := ( 3, 4)( 5,10)( 6, 9)( 7,11)( 8,12)(15,16)(17,33)(18,34)(19,36)(20,35)(21,42)(22,41)(23,43)(24,44)(25,38)(26,37)(27,39)(28,40)(29,45)(30,46)(31,48)(32,47)(51,52)(53,58)(54,57)(55,59)(56,60)(63,64)(65,81)(66,82)(67,84)(68,83)(69,90)(70,89)(71,91)(72,92)(73,86)(74,85)(75,87)(76,88)(77,93)(78,94)(79,96)(80,95);; s2 := ( 1,89)( 2,92)( 3,91)( 4,90)( 5,87)( 6,86)( 7,85)( 8,88)( 9,81)(10,84)(11,83)(12,82)(13,93)(14,96)(15,95)(16,94)(17,73)(18,76)(19,75)(20,74)(21,71)(22,70)(23,69)(24,72)(25,65)(26,68)(27,67)(28,66)(29,77)(30,80)(31,79)(32,78)(33,57)(34,60)(35,59)(36,58)(37,55)(38,54)(39,53)(40,56)(41,49)(42,52)(43,51)(44,50)(45,61)(46,64)(47,63)(48,62);; 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*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(96)!( 1, 9)( 2,10)( 3,11)( 4,12)( 5,16)( 6,15)( 7,14)( 8,13)(17,25)(18,26)(19,27)(20,28)(21,32)(22,31)(23,30)(24,29)(33,41)(34,42)(35,43)(36,44)(37,48)(38,47)(39,46)(40,45)(49,57)(50,58)(51,59)(52,60)(53,64)(54,63)(55,62)(56,61)(65,73)(66,74)(67,75)(68,76)(69,80)(70,79)(71,78)(72,77)(81,89)(82,90)(83,91)(84,92)(85,96)(86,95)(87,94)(88,93); s1 := Sym(96)!( 3, 4)( 5,10)( 6, 9)( 7,11)( 8,12)(15,16)(17,33)(18,34)(19,36)(20,35)(21,42)(22,41)(23,43)(24,44)(25,38)(26,37)(27,39)(28,40)(29,45)(30,46)(31,48)(32,47)(51,52)(53,58)(54,57)(55,59)(56,60)(63,64)(65,81)(66,82)(67,84)(68,83)(69,90)(70,89)(71,91)(72,92)(73,86)(74,85)(75,87)(76,88)(77,93)(78,94)(79,96)(80,95); s2 := Sym(96)!( 1,89)( 2,92)( 3,91)( 4,90)( 5,87)( 6,86)( 7,85)( 8,88)( 9,81)(10,84)(11,83)(12,82)(13,93)(14,96)(15,95)(16,94)(17,73)(18,76)(19,75)(20,74)(21,71)(22,70)(23,69)(24,72)(25,65)(26,68)(27,67)(28,66)(29,77)(30,80)(31,79)(32,78)(33,57)(34,60)(35,59)(36,58)(37,55)(38,54)(39,53)(40,56)(41,49)(42,52)(43,51)(44,50)(45,61)(46,64)(47,63)(48,62); 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*s2*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0 >;
References
None.
to this polytope.