Overview
- Group
- SmallGroup(1920,236184)
- Rank
- 6
- Schläfli Type
- {2,6,20,2,2}
- Vertices, edges, …
- 2, 6, 60, 20, 2, 2
- Order of s0s1s2s3s4s5
- 60
- 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
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 := (1,2);; s1 := ( 8,13)( 9,14)(10,15)(11,16)(12,17)(23,28)(24,29)(25,30)(26,31)(27,32)(38,43)(39,44)(40,45)(41,46)(42,47)(53,58)(54,59)(55,60)(56,61)(57,62);; s2 := ( 3, 8)( 4,12)( 5,11)( 6,10)( 7, 9)(14,17)(15,16)(18,23)(19,27)(20,26)(21,25)(22,24)(29,32)(30,31)(33,53)(34,57)(35,56)(36,55)(37,54)(38,48)(39,52)(40,51)(41,50)(42,49)(43,58)(44,62)(45,61)(46,60)(47,59);; s3 := ( 3,34)( 4,33)( 5,37)( 6,36)( 7,35)( 8,39)( 9,38)(10,42)(11,41)(12,40)(13,44)(14,43)(15,47)(16,46)(17,45)(18,49)(19,48)(20,52)(21,51)(22,50)(23,54)(24,53)(25,57)(26,56)(27,55)(28,59)(29,58)(30,62)(31,61)(32,60);; s4 := (63,64);; s5 := (65,66);; 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,
s4*s5*s4*s5, s1*s2*s3*s2*s1*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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(66)!(1,2); s1 := Sym(66)!( 8,13)( 9,14)(10,15)(11,16)(12,17)(23,28)(24,29)(25,30)(26,31)(27,32)(38,43)(39,44)(40,45)(41,46)(42,47)(53,58)(54,59)(55,60)(56,61)(57,62); s2 := Sym(66)!( 3, 8)( 4,12)( 5,11)( 6,10)( 7, 9)(14,17)(15,16)(18,23)(19,27)(20,26)(21,25)(22,24)(29,32)(30,31)(33,53)(34,57)(35,56)(36,55)(37,54)(38,48)(39,52)(40,51)(41,50)(42,49)(43,58)(44,62)(45,61)(46,60)(47,59); s3 := Sym(66)!( 3,34)( 4,33)( 5,37)( 6,36)( 7,35)( 8,39)( 9,38)(10,42)(11,41)(12,40)(13,44)(14,43)(15,47)(16,46)(17,45)(18,49)(19,48)(20,52)(21,51)(22,50)(23,54)(24,53)(25,57)(26,56)(27,55)(28,59)(29,58)(30,62)(31,61)(32,60); s4 := Sym(66)!(63,64); s5 := Sym(66)!(65,66); poly := sub<Sym(66)|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, s4*s5*s4*s5, s1*s2*s3*s2*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;