Overview
- Group
- SmallGroup(480,948)
- Rank
- 4
- Schläfli Type
- {3,12,3}
- Vertices, edges, …
- 5, 40, 40, 5
- Order of s0s1s2s3
- 10
- Order of s0s1s2s3s2s1
- 12
- Also known as
- if this polytope has a name.
Special Properties
- Universal
- Orientable
- Self-Dual
Quotients maximal quotients in bold
2-fold
4-fold
Covers minimal covers in bold
2-fold
3-fold
4-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 1,11)( 2,24)( 3, 9)( 4,10)( 5,12)( 6,25)( 7,40)( 8,39)(13,19)(14,36)(15,27)(16,28)(17,18)(20,22)(26,35)(29,38)(30,37)(31,32)(33,34);; s1 := ( 1, 2)( 3,15)( 4,16)( 5, 6)( 7, 9)( 8,10)(11,31)(12,34)(14,17)(18,20)(19,23)(21,35)(22,36)(24,32)(25,33)(27,40)(28,39)(29,38)(30,37);; s2 := ( 2, 5)( 3, 9)( 4,10)( 7,14)( 8,13)(12,24)(15,26)(16,17)(18,28)(19,39)(21,23)(27,35)(29,33)(30,32)(31,37)(34,38)(36,40);; s3 := ( 1,40)( 2,27)( 3,32)( 4,33)( 5,39)( 6,28)( 7,11)( 8,12)( 9,31)(10,34)(13,26)(15,24)(16,25)(19,35)(21,23)(29,38)(30,37);; poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3, s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s3*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(40)!( 1,11)( 2,24)( 3, 9)( 4,10)( 5,12)( 6,25)( 7,40)( 8,39)(13,19)(14,36)(15,27)(16,28)(17,18)(20,22)(26,35)(29,38)(30,37)(31,32)(33,34); s1 := Sym(40)!( 1, 2)( 3,15)( 4,16)( 5, 6)( 7, 9)( 8,10)(11,31)(12,34)(14,17)(18,20)(19,23)(21,35)(22,36)(24,32)(25,33)(27,40)(28,39)(29,38)(30,37); s2 := Sym(40)!( 2, 5)( 3, 9)( 4,10)( 7,14)( 8,13)(12,24)(15,26)(16,17)(18,28)(19,39)(21,23)(27,35)(29,33)(30,32)(31,37)(34,38)(36,40); s3 := Sym(40)!( 1,40)( 2,27)( 3,32)( 4,33)( 5,39)( 6,28)( 7,11)( 8,12)( 9,31)(10,34)(13,26)(15,24)(16,25)(19,35)(21,23)(29,38)(30,37); poly := sub<Sym(40)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3, s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1, s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s3*s1*s2 >;
References
None.
to this polytope.