Overview
- Group
- SmallGroup(1440,5284)
- Rank
- 5
- Schläfli Type
- {20,6,2,3}
- Vertices, edges, …
- 20, 60, 6, 3, 3
- Order of s0s1s2s3s4
- 60
- 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
6-fold
10-fold
12-fold
15-fold
20-fold
30-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := ( 2, 5)( 3, 4)( 7,10)( 8, 9)(12,15)(13,14)(17,20)(18,19)(22,25)(23,24)(27,30)(28,29)(31,46)(32,50)(33,49)(34,48)(35,47)(36,51)(37,55)(38,54)(39,53)(40,52)(41,56)(42,60)(43,59)(44,58)(45,57);; s1 := ( 1,32)( 2,31)( 3,35)( 4,34)( 5,33)( 6,42)( 7,41)( 8,45)( 9,44)(10,43)(11,37)(12,36)(13,40)(14,39)(15,38)(16,47)(17,46)(18,50)(19,49)(20,48)(21,57)(22,56)(23,60)(24,59)(25,58)(26,52)(27,51)(28,55)(29,54)(30,53);; s2 := ( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5,10)(16,21)(17,22)(18,23)(19,24)(20,25)(31,36)(32,37)(33,38)(34,39)(35,40)(46,51)(47,52)(48,53)(49,54)(50,55);; s3 := (62,63);; s4 := (61,62);; 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,
s3*s4*s3*s4*s3*s4, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(63)!( 2, 5)( 3, 4)( 7,10)( 8, 9)(12,15)(13,14)(17,20)(18,19)(22,25)(23,24)(27,30)(28,29)(31,46)(32,50)(33,49)(34,48)(35,47)(36,51)(37,55)(38,54)(39,53)(40,52)(41,56)(42,60)(43,59)(44,58)(45,57); s1 := Sym(63)!( 1,32)( 2,31)( 3,35)( 4,34)( 5,33)( 6,42)( 7,41)( 8,45)( 9,44)(10,43)(11,37)(12,36)(13,40)(14,39)(15,38)(16,47)(17,46)(18,50)(19,49)(20,48)(21,57)(22,56)(23,60)(24,59)(25,58)(26,52)(27,51)(28,55)(29,54)(30,53); s2 := Sym(63)!( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5,10)(16,21)(17,22)(18,23)(19,24)(20,25)(31,36)(32,37)(33,38)(34,39)(35,40)(46,51)(47,52)(48,53)(49,54)(50,55); s3 := Sym(63)!(62,63); s4 := Sym(63)!(61,62); poly := sub<Sym(63)|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, s3*s4*s3*s4*s3*s4, s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;