Overview
- Group
- SmallGroup(1920,235343)
- Rank
- 5
- Schläfli Type
- {8,2,10,6}
- Vertices, edges, …
- 8, 8, 10, 30, 6
- Order of s0s1s2s3s4
- 120
- Order of s0s1s2s3s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
5-fold
6-fold
10-fold
12-fold
15-fold
20-fold
24-fold
30-fold
40-fold
60-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (2,3)(4,5)(6,7);; s1 := (1,2)(3,4)(5,6)(7,8);; s2 := (13,14)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38);; s3 := ( 9,13)(10,17)(11,21)(12,19)(14,23)(15,27)(16,25)(18,29)(20,33)(22,31)(26,37)(28,35)(32,34)(36,38);; s4 := ( 9,15)(10,11)(12,16)(13,25)(14,26)(17,19)(18,20)(21,27)(22,28)(23,35)(24,36)(29,31)(30,32)(33,37)(34,38);; poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(38)!(2,3)(4,5)(6,7); s1 := Sym(38)!(1,2)(3,4)(5,6)(7,8); s2 := Sym(38)!(13,14)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38); s3 := Sym(38)!( 9,13)(10,17)(11,21)(12,19)(14,23)(15,27)(16,25)(18,29)(20,33)(22,31)(26,37)(28,35)(32,34)(36,38); s4 := Sym(38)!( 9,15)(10,11)(12,16)(13,25)(14,26)(17,19)(18,20)(21,27)(22,28)(23,35)(24,36)(29,31)(30,32)(33,37)(34,38); poly := sub<Sym(38)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;