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