Overview
- Group
- SmallGroup(1792,1083341)
- Rank
- 6
- Schläfli Type
- {2,2,2,14,8}
- Vertices, edges, …
- 2, 2, 2, 14, 56, 8
- Order of s0s1s2s3s4s5
- 56
- 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
4-fold
7-fold
8-fold
14-fold
28-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := (3,4);; s2 := (5,6);; s3 := ( 8,13)( 9,12)(10,11)(15,20)(16,19)(17,18)(22,27)(23,26)(24,25)(29,34)(30,33)(31,32)(36,41)(37,40)(38,39)(43,48)(44,47)(45,46)(50,55)(51,54)(52,53)(57,62)(58,61)(59,60);; s4 := ( 7, 8)( 9,13)(10,12)(14,15)(16,20)(17,19)(21,29)(22,28)(23,34)(24,33)(25,32)(26,31)(27,30)(35,50)(36,49)(37,55)(38,54)(39,53)(40,52)(41,51)(42,57)(43,56)(44,62)(45,61)(46,60)(47,59)(48,58);; s5 := ( 7,35)( 8,36)( 9,37)(10,38)(11,39)(12,40)(13,41)(14,42)(15,43)(16,44)(17,45)(18,46)(19,47)(20,48)(21,56)(22,57)(23,58)(24,59)(25,60)(26,61)(27,62)(28,49)(29,50)(30,51)(31,52)(32,53)(33,54)(34,55);; 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, s2*s3*s2*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, s3*s4*s5*s4*s3*s4*s5*s4,
s4*s5*s4*s5*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*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(62)!(1,2); s1 := Sym(62)!(3,4); s2 := Sym(62)!(5,6); s3 := Sym(62)!( 8,13)( 9,12)(10,11)(15,20)(16,19)(17,18)(22,27)(23,26)(24,25)(29,34)(30,33)(31,32)(36,41)(37,40)(38,39)(43,48)(44,47)(45,46)(50,55)(51,54)(52,53)(57,62)(58,61)(59,60); s4 := Sym(62)!( 7, 8)( 9,13)(10,12)(14,15)(16,20)(17,19)(21,29)(22,28)(23,34)(24,33)(25,32)(26,31)(27,30)(35,50)(36,49)(37,55)(38,54)(39,53)(40,52)(41,51)(42,57)(43,56)(44,62)(45,61)(46,60)(47,59)(48,58); s5 := Sym(62)!( 7,35)( 8,36)( 9,37)(10,38)(11,39)(12,40)(13,41)(14,42)(15,43)(16,44)(17,45)(18,46)(19,47)(20,48)(21,56)(22,57)(23,58)(24,59)(25,60)(26,61)(27,62)(28,49)(29,50)(30,51)(31,52)(32,53)(33,54)(34,55); poly := sub<Sym(62)|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, s2*s3*s2*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, s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*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*s3*s4*s3*s4*s3*s4*s3*s4 >;