Overview
- Group
- SmallGroup(384,18032)
- Rank
- 3
- Schläfli Type
- {6,8}
- Vertices, edges, …
- 24, 96, 32
- Order of s0s1s2
- 24
- Order of s0s1s2s1
- 4
- 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
12-fold
16-fold
24-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)^2*s2*(s1*s0)^2*s2> of order 2
16 facets
- 16 of {6}*12
12 vertex figures
- 12 of {8}*16
P/N, where N=<s0*s1*s2*s1*s0*(s1*s2)^2> of order 2
16 facets
- 16 of {6}*12
12 vertex figures
- 12 of {8}*16
P/N, where N=<s0*s1*s0*(s2*s1)^2*s0*s2*s1*s0*s2> of order 2
16 facets
- 16 of {6}*12
12 vertex figures
- 12 of {8}*16
P/N, where N=<(s0*s1)^2*s2*(s1*s0)^2*s2, s0*s1*s2*s1*s0*(s2*s1)^2*s2> of order 4
8 facets
- 8 of {6}*12
6 vertex figures
- 6 of {8}*16
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,21)(18,23)(19,22)(20,24)(26,27)(29,33)(30,35)(31,34)(32,36)(38,39)(41,45)(42,47)(43,46)(44,48)(50,51)(53,57)(54,59)(55,58)(56,60)(62,63)(65,69)(66,71)(67,70)(68,72)(74,75)(77,81)(78,83)(79,82)(80,84)(86,87)(89,93)(90,95)(91,94)(92,96);; s1 := ( 1, 5)( 2, 6)( 3, 8)( 4, 7)(11,12)(13,17)(14,18)(15,20)(16,19)(23,24)(25,41)(26,42)(27,44)(28,43)(29,37)(30,38)(31,40)(32,39)(33,45)(34,46)(35,48)(36,47)(49,77)(50,78)(51,80)(52,79)(53,73)(54,74)(55,76)(56,75)(57,81)(58,82)(59,84)(60,83)(61,89)(62,90)(63,92)(64,91)(65,85)(66,86)(67,88)(68,87)(69,93)(70,94)(71,96)(72,95);; s2 := ( 1,52)( 2,51)( 3,50)( 4,49)( 5,56)( 6,55)( 7,54)( 8,53)( 9,60)(10,59)(11,58)(12,57)(13,64)(14,63)(15,62)(16,61)(17,68)(18,67)(19,66)(20,65)(21,72)(22,71)(23,70)(24,69)(25,88)(26,87)(27,86)(28,85)(29,92)(30,91)(31,90)(32,89)(33,96)(34,95)(35,94)(36,93)(37,76)(38,75)(39,74)(40,73)(41,80)(42,79)(43,78)(44,77)(45,84)(46,83)(47,82)(48,81);; 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*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
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)!( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,21)(18,23)(19,22)(20,24)(26,27)(29,33)(30,35)(31,34)(32,36)(38,39)(41,45)(42,47)(43,46)(44,48)(50,51)(53,57)(54,59)(55,58)(56,60)(62,63)(65,69)(66,71)(67,70)(68,72)(74,75)(77,81)(78,83)(79,82)(80,84)(86,87)(89,93)(90,95)(91,94)(92,96); s1 := Sym(96)!( 1, 5)( 2, 6)( 3, 8)( 4, 7)(11,12)(13,17)(14,18)(15,20)(16,19)(23,24)(25,41)(26,42)(27,44)(28,43)(29,37)(30,38)(31,40)(32,39)(33,45)(34,46)(35,48)(36,47)(49,77)(50,78)(51,80)(52,79)(53,73)(54,74)(55,76)(56,75)(57,81)(58,82)(59,84)(60,83)(61,89)(62,90)(63,92)(64,91)(65,85)(66,86)(67,88)(68,87)(69,93)(70,94)(71,96)(72,95); s2 := Sym(96)!( 1,52)( 2,51)( 3,50)( 4,49)( 5,56)( 6,55)( 7,54)( 8,53)( 9,60)(10,59)(11,58)(12,57)(13,64)(14,63)(15,62)(16,61)(17,68)(18,67)(19,66)(20,65)(21,72)(22,71)(23,70)(24,69)(25,88)(26,87)(27,86)(28,85)(29,92)(30,91)(31,90)(32,89)(33,96)(34,95)(35,94)(36,93)(37,76)(38,75)(39,74)(40,73)(41,80)(42,79)(43,78)(44,77)(45,84)(46,83)(47,82)(48,81); 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*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References
None.
to this polytope.