Overview
- Group
- SmallGroup(1920,236178)
- Rank
- 6
- Schläfli Type
- {2,2,4,10,6}
- Vertices, edges, …
- 2, 2, 4, 20, 30, 6
- 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 := (3,4);; s2 := (35,50)(36,51)(37,52)(38,53)(39,54)(40,55)(41,56)(42,57)(43,58)(44,59)(45,60)(46,61)(47,62)(48,63)(49,64);; s3 := ( 5,35)( 6,39)( 7,38)( 8,37)( 9,36)(10,40)(11,44)(12,43)(13,42)(14,41)(15,45)(16,49)(17,48)(18,47)(19,46)(20,50)(21,54)(22,53)(23,52)(24,51)(25,55)(26,59)(27,58)(28,57)(29,56)(30,60)(31,64)(32,63)(33,62)(34,61);; s4 := ( 5, 6)( 7, 9)(10,16)(11,15)(12,19)(13,18)(14,17)(20,21)(22,24)(25,31)(26,30)(27,34)(28,33)(29,32)(35,36)(37,39)(40,46)(41,45)(42,49)(43,48)(44,47)(50,51)(52,54)(55,61)(56,60)(57,64)(58,63)(59,62);; s5 := ( 5,10)( 6,11)( 7,12)( 8,13)( 9,14)(20,25)(21,26)(22,27)(23,28)(24,29)(35,40)(36,41)(37,42)(38,43)(39,44)(50,55)(51,56)(52,57)(53,58)(54,59);; 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, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(64)!(1,2); s1 := Sym(64)!(3,4); s2 := Sym(64)!(35,50)(36,51)(37,52)(38,53)(39,54)(40,55)(41,56)(42,57)(43,58)(44,59)(45,60)(46,61)(47,62)(48,63)(49,64); s3 := Sym(64)!( 5,35)( 6,39)( 7,38)( 8,37)( 9,36)(10,40)(11,44)(12,43)(13,42)(14,41)(15,45)(16,49)(17,48)(18,47)(19,46)(20,50)(21,54)(22,53)(23,52)(24,51)(25,55)(26,59)(27,58)(28,57)(29,56)(30,60)(31,64)(32,63)(33,62)(34,61); s4 := Sym(64)!( 5, 6)( 7, 9)(10,16)(11,15)(12,19)(13,18)(14,17)(20,21)(22,24)(25,31)(26,30)(27,34)(28,33)(29,32)(35,36)(37,39)(40,46)(41,45)(42,49)(43,48)(44,47)(50,51)(52,54)(55,61)(56,60)(57,64)(58,63)(59,62); s5 := Sym(64)!( 5,10)( 6,11)( 7,12)( 8,13)( 9,14)(20,25)(21,26)(22,27)(23,28)(24,29)(35,40)(36,41)(37,42)(38,43)(39,44)(50,55)(51,56)(52,57)(53,58)(54,59); poly := sub<Sym(64)|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, s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;