Overview
- Group
- SmallGroup(1920,235343)
- Rank
- 5
- Schläfli Type
- {6,10,2,8}
- Vertices, edges, …
- 6, 30, 10, 8, 8
- 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 := ( 3, 4)( 7, 8)(11,13)(12,14)(17,19)(18,20)(23,25)(24,26)(27,29)(28,30);; s1 := ( 1, 3)( 2, 7)( 5,12)( 6,11)( 9,18)(10,17)(13,14)(15,24)(16,23)(19,20)(21,28)(22,27)(25,26)(29,30);; s2 := ( 1, 9)( 2, 5)( 3,17)( 4,19)( 6,21)( 7,11)( 8,13)(10,15)(12,27)(14,29)(16,22)(18,23)(20,25)(24,28)(26,30);; s3 := (32,33)(34,35)(36,37);; s4 := (31,32)(33,34)(35,36)(37,38);; 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,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(38)!( 3, 4)( 7, 8)(11,13)(12,14)(17,19)(18,20)(23,25)(24,26)(27,29)(28,30); s1 := Sym(38)!( 1, 3)( 2, 7)( 5,12)( 6,11)( 9,18)(10,17)(13,14)(15,24)(16,23)(19,20)(21,28)(22,27)(25,26)(29,30); s2 := Sym(38)!( 1, 9)( 2, 5)( 3,17)( 4,19)( 6,21)( 7,11)( 8,13)(10,15)(12,27)(14,29)(16,22)(18,23)(20,25)(24,28)(26,30); s3 := Sym(38)!(32,33)(34,35)(36,37); s4 := Sym(38)!(31,32)(33,34)(35,36)(37,38); 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, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;