Overview
- Group
- SmallGroup(1920,236178)
- Rank
- 6
- Schläfli Type
- {4,2,6,10,2}
- Vertices, edges, …
- 4, 4, 6, 30, 10, 2
- Order of s0s1s2s3s4s5
- 60
- Order of s0s1s2s3s4s5s4s3s2s1
- 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
5-fold
6-fold
10-fold
12-fold
15-fold
20-fold
30-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (2,3);; s1 := (1,2)(3,4);; s2 := ( 7, 8)(11,12)(15,17)(16,18)(21,23)(22,24)(27,29)(28,30)(31,33)(32,34);; s3 := ( 5, 7)( 6,11)( 9,16)(10,15)(13,22)(14,21)(17,18)(19,28)(20,27)(23,24)(25,32)(26,31)(29,30)(33,34);; s4 := ( 5,13)( 6, 9)( 7,21)( 8,23)(10,25)(11,15)(12,17)(14,19)(16,31)(18,33)(20,26)(22,27)(24,29)(28,32)(30,34);; s5 := (35,36);; poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
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, s0*s5*s0*s5, s1*s5*s1*s5,
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5,
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s4*s3*s2*s3*s4*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(36)!(2,3); s1 := Sym(36)!(1,2)(3,4); s2 := Sym(36)!( 7, 8)(11,12)(15,17)(16,18)(21,23)(22,24)(27,29)(28,30)(31,33)(32,34); s3 := Sym(36)!( 5, 7)( 6,11)( 9,16)(10,15)(13,22)(14,21)(17,18)(19,28)(20,27)(23,24)(25,32)(26,31)(29,30)(33,34); s4 := Sym(36)!( 5,13)( 6, 9)( 7,21)( 8,23)(10,25)(11,15)(12,17)(14,19)(16,31)(18,33)(20,26)(22,27)(24,29)(28,32)(30,34); s5 := Sym(36)!(35,36); poly := sub<Sym(36)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 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, s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5, s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s4*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;