Overview
- Group
- SmallGroup(96,193)
- Rank
- 3
- Schläfli Type
- {3,12}
- Vertices, edges, …
- 4, 24, 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
Covers minimal covers in bold
2-fold
3-fold
4-fold
5-fold
6-fold
7-fold
8-fold
9-fold
10-fold
11-fold
12-fold
- {3,12}*1152a
- {12,12}*1152d
- {12,12}*1152e
- {12,12}*1152g
- {6,12}*1152a
- {6,12}*1152e
- {12,12}*1152p
- {3,12}*1152b
13-fold
14-fold
15-fold
17-fold
18-fold
19-fold
20-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 4, 5)( 6,19)( 7,22)( 9,14)(10,13)(11,31)(12,34)(15,37)(16,38)(17,23)(18,20)(21,42)(24,41)(25,26)(27,43)(28,45)(29,32)(30,35)(33,47)(36,48)(39,40);; s1 := ( 1, 4)( 2,13)( 3, 9)( 6,42)( 7,41)( 8,25)(10,14)(11,47)(12,48)(15,40)(16,39)(17,24)(18,21)(19,20)(22,23)(27,44)(28,46)(29,33)(30,36)(31,32)(34,35)(37,38);; s2 := ( 1,44)( 2,39)( 3,40)( 4,33)( 5,47)( 6,12)( 7,11)( 8,46)( 9,21)(10,41)(13,24)(14,42)(15,30)(16,29)(17,28)(18,27)(19,34)(20,43)(22,31)(23,45)(25,36)(26,48)(32,38)(35,37);; 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,
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(48)!( 2, 3)( 4, 5)( 6,19)( 7,22)( 9,14)(10,13)(11,31)(12,34)(15,37)(16,38)(17,23)(18,20)(21,42)(24,41)(25,26)(27,43)(28,45)(29,32)(30,35)(33,47)(36,48)(39,40); s1 := Sym(48)!( 1, 4)( 2,13)( 3, 9)( 6,42)( 7,41)( 8,25)(10,14)(11,47)(12,48)(15,40)(16,39)(17,24)(18,21)(19,20)(22,23)(27,44)(28,46)(29,33)(30,36)(31,32)(34,35)(37,38); s2 := Sym(48)!( 1,44)( 2,39)( 3,40)( 4,33)( 5,47)( 6,12)( 7,11)( 8,46)( 9,21)(10,41)(13,24)(14,42)(15,30)(16,29)(17,28)(18,27)(19,34)(20,43)(22,31)(23,45)(25,36)(26,48)(32,38)(35,37); poly := sub<Sym(48)|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, s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1 >;
References
None.
to this polytope.