Overview
- Group
- SmallGroup(1200,1006)
- Rank
- 5
- Schläfli Type
- {5,10,2,6}
- Vertices, edges, …
- 5, 25, 10, 6, 6
- Order of s0s1s2s3s4
- 30
- 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
5-fold
10-fold
15-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 4, 5)( 6, 9)( 7,11)( 8,10)(12,13)(14,19)(15,18)(16,21)(17,20)(22,25)(23,24);; s1 := ( 1, 7)( 2, 4)( 3,14)( 5,16)( 6,10)( 8,12)( 9,18)(11,22)(13,17)(15,20)(19,24)(21,23);; s2 := ( 4, 5)( 7, 8)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25);; s3 := (28,29)(30,31);; s4 := (26,30)(27,28)(29,31);; 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,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(31)!( 2, 3)( 4, 5)( 6, 9)( 7,11)( 8,10)(12,13)(14,19)(15,18)(16,21)(17,20)(22,25)(23,24); s1 := Sym(31)!( 1, 7)( 2, 4)( 3,14)( 5,16)( 6,10)( 8,12)( 9,18)(11,22)(13,17)(15,20)(19,24)(21,23); s2 := Sym(31)!( 4, 5)( 7, 8)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25); s3 := Sym(31)!(28,29)(30,31); s4 := Sym(31)!(26,30)(27,28)(29,31); poly := sub<Sym(31)|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, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;