Overview
- Group
- SmallGroup(192,1481)
- Rank
- 4
- Schläfli Type
- {2,3,8}
- Vertices, edges, …
- 2, 6, 24, 16
- Order of s0s1s2s3
- 12
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
4-fold
8-fold
Covers minimal covers in bold
2-fold
3-fold
4-fold
5-fold
6-fold
7-fold
9-fold
10-fold
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 5)( 6, 7)( 8,21)( 9,24)(11,16)(12,15)(13,33)(14,36)(17,39)(18,40)(19,25)(20,22)(23,44)(26,43)(27,28)(29,45)(30,47)(31,34)(32,37)(35,49)(38,50)(41,42);; s2 := ( 3, 6)( 4,15)( 5,11)( 8,44)( 9,43)(10,27)(12,16)(13,49)(14,50)(17,42)(18,41)(19,26)(20,23)(21,22)(24,25)(29,46)(30,48)(31,35)(32,38)(33,34)(36,37)(39,40);; s3 := ( 3,46)( 4,42)( 5,41)( 6,49)( 7,35)( 8,36)( 9,33)(10,48)(11,44)(12,26)(13,24)(14,21)(15,43)(16,23)(17,37)(18,34)(19,47)(20,45)(22,29)(25,30)(27,50)(28,38)(31,40)(32,39);; poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(50)!(1,2); s1 := Sym(50)!( 4, 5)( 6, 7)( 8,21)( 9,24)(11,16)(12,15)(13,33)(14,36)(17,39)(18,40)(19,25)(20,22)(23,44)(26,43)(27,28)(29,45)(30,47)(31,34)(32,37)(35,49)(38,50)(41,42); s2 := Sym(50)!( 3, 6)( 4,15)( 5,11)( 8,44)( 9,43)(10,27)(12,16)(13,49)(14,50)(17,42)(18,41)(19,26)(20,23)(21,22)(24,25)(29,46)(30,48)(31,35)(32,38)(33,34)(36,37)(39,40); s3 := Sym(50)!( 3,46)( 4,42)( 5,41)( 6,49)( 7,35)( 8,36)( 9,33)(10,48)(11,44)(12,26)(13,24)(14,21)(15,43)(16,23)(17,37)(18,34)(19,47)(20,45)(22,29)(25,30)(27,50)(28,38)(31,40)(32,39); poly := sub<Sym(50)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2 >;