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