Overview
- Group
- SmallGroup(1152,98785)
- Rank
- 5
- Schläfli Type
- {3,2,8,12}
- Vertices, edges, …
- 3, 3, 8, 48, 12
- 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
12-fold
16-fold
24-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (2,3);; s1 := (1,2);; s2 := ( 4,16)( 5,17)( 6,18)( 7,19)( 8,20)( 9,21)(10,25)(11,26)(12,27)(13,22)(14,23)(15,24);; s3 := ( 5, 6)( 8, 9)(10,13)(11,15)(12,14)(16,22)(17,24)(18,23)(19,25)(20,27)(21,26);; s4 := ( 4, 5)( 7, 8)(10,14)(11,13)(12,15)(16,17)(19,20)(22,26)(23,25)(24,27);; 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,
s0*s1*s0*s1*s0*s1, s2*s3*s4*s2*s3*s2*s3*s4*s2*s3,
s2*s3*s2*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*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(27)!(2,3); s1 := Sym(27)!(1,2); s2 := Sym(27)!( 4,16)( 5,17)( 6,18)( 7,19)( 8,20)( 9,21)(10,25)(11,26)(12,27)(13,22)(14,23)(15,24); s3 := Sym(27)!( 5, 6)( 8, 9)(10,13)(11,15)(12,14)(16,22)(17,24)(18,23)(19,25)(20,27)(21,26); s4 := Sym(27)!( 4, 5)( 7, 8)(10,14)(11,13)(12,15)(16,17)(19,20)(22,26)(23,25)(24,27); poly := sub<Sym(27)|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, s0*s1*s0*s1*s0*s1, s2*s3*s4*s2*s3*s2*s3*s4*s2*s3, s2*s3*s2*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*s3*s4*s3*s4 >;