Overview
- Group
- SmallGroup(1920,235343)
- Rank
- 6
- Schläfli Type
- {2,8,6,2,5}
- Vertices, edges, …
- 2, 8, 24, 6, 5, 5
- Order of s0s1s2s3s4s5
- 120
- 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
4-fold
6-fold
8-fold
12-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 7)( 8,11)( 9,12)(10,13)(14,17)(15,18)(16,19)(20,23)(21,24);; s2 := ( 3, 4)( 5, 9)( 6, 8)( 7,10)(11,15)(12,14)(13,16)(17,21)(18,20)(19,22)(23,26)(24,25);; s3 := ( 3, 5)( 4, 8)( 7,11)(10,14)(13,17)(16,20)(19,23)(22,25);; s4 := (28,29)(30,31);; s5 := (27,28)(29,30);; 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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s3*s4*s3*s4, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s1*s2*s3*s2*s1*s2*s3*s2, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(31)!(1,2); s1 := Sym(31)!( 4, 7)( 8,11)( 9,12)(10,13)(14,17)(15,18)(16,19)(20,23)(21,24); s2 := Sym(31)!( 3, 4)( 5, 9)( 6, 8)( 7,10)(11,15)(12,14)(13,16)(17,21)(18,20)(19,22)(23,26)(24,25); s3 := Sym(31)!( 3, 5)( 4, 8)( 7,11)(10,14)(13,17)(16,20)(19,23)(22,25); s4 := Sym(31)!(28,29)(30,31); s5 := Sym(31)!(27,28)(29,30); poly := sub<Sym(31)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, s1*s2*s3*s2*s1*s2*s3*s2, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;