Overview
- Group
- SmallGroup(1152,152548)
- Rank
- 5
- Schläfli Type
- {6,2,6,8}
- Vertices, edges, …
- 6, 6, 6, 24, 8
- Order of s0s1s2s3s4
- 24
- 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
6-fold
8-fold
9-fold
12-fold
16-fold
18-fold
24-fold
36-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (3,4)(5,6);; s1 := (1,5)(2,3)(4,6);; s2 := ( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(29,30);; s3 := ( 7, 9)( 8,15)(11,12)(13,16)(14,21)(17,18)(19,22)(20,27)(23,24)(25,28)(26,29);; s4 := ( 7, 8)( 9,12)(10,13)(11,14)(15,18)(16,19)(17,20)(21,24)(22,25)(23,26)(27,29)(28,30);; 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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(30)!(3,4)(5,6); s1 := Sym(30)!(1,5)(2,3)(4,6); s2 := Sym(30)!( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(29,30); s3 := Sym(30)!( 7, 9)( 8,15)(11,12)(13,16)(14,21)(17,18)(19,22)(20,27)(23,24)(25,28)(26,29); s4 := Sym(30)!( 7, 8)( 9,12)(10,13)(11,14)(15,18)(16,19)(17,20)(21,24)(22,25)(23,26)(27,29)(28,30); poly := sub<Sym(30)|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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 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 >;