Overview
- Group
- SmallGroup(768,364865)
- Rank
- 5
- Schläfli Type
- {4,2,12,4}
- Vertices, edges, …
- 4, 4, 12, 24, 4
- Order of s0s1s2s3s4
- 12
- 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)(3,4);; s2 := ( 6, 7)( 8, 9)(10,14)(12,16)(13,15)(19,24)(20,23)(21,22)(25,26)(27,28);; s3 := ( 5,12)( 6, 8)( 7,21)( 9,13)(10,27)(11,15)(14,25)(16,22)(17,23)(18,19)(20,28)(24,26);; s4 := ( 6,10)( 7,14)(12,19)(13,20)(15,23)(16,24);; 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*s0*s1, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*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(28)!(2,3); s1 := Sym(28)!(1,2)(3,4); s2 := Sym(28)!( 6, 7)( 8, 9)(10,14)(12,16)(13,15)(19,24)(20,23)(21,22)(25,26)(27,28); s3 := Sym(28)!( 5,12)( 6, 8)( 7,21)( 9,13)(10,27)(11,15)(14,25)(16,22)(17,23)(18,19)(20,28)(24,26); s4 := Sym(28)!( 6,10)( 7,14)(12,19)(13,20)(15,23)(16,24); poly := sub<Sym(28)|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*s0*s1, s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;