Overview
- Group
- SmallGroup(768,1090143)
- Rank
- 6
- Schläfli Type
- {2,2,12,4,2}
- Vertices, edges, …
- 2, 2, 12, 24, 4, 2
- Order of s0s1s2s3s4s5
- 12
- Order of s0s1s2s3s4s5s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
2-fold
4-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := (3,4);; s2 := ( 6, 7)( 8, 9)(10,20)(12,16)(13,15)(14,28)(17,33)(18,36)(19,21)(22,38)(23,24)(25,41)(26,44)(27,34)(29,32)(30,48)(31,45)(35,47)(39,50)(40,42)(43,52)(46,49);; s3 := ( 5,12)( 6, 8)( 7,23)( 9,13)(10,47)(11,15)(14,38)(16,24)(17,52)(18,46)(19,30)(20,29)(21,33)(22,27)(25,48)(26,37)(28,42)(31,51)(32,43)(34,41)(35,40)(36,45)(39,49)(44,50);; s4 := ( 5,51)( 6,49)( 7,46)( 8,52)( 9,43)(10,41)(11,37)(12,48)(13,35)(14,28)(15,47)(16,30)(17,33)(18,42)(19,50)(20,25)(21,39)(22,24)(23,38)(26,34)(27,44)(29,31)(32,45)(36,40);; s5 := (53,54);; 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,
s4*s5*s4*s5, s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*s3,
s3*s2*s3*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(54)!(1,2); s1 := Sym(54)!(3,4); s2 := Sym(54)!( 6, 7)( 8, 9)(10,20)(12,16)(13,15)(14,28)(17,33)(18,36)(19,21)(22,38)(23,24)(25,41)(26,44)(27,34)(29,32)(30,48)(31,45)(35,47)(39,50)(40,42)(43,52)(46,49); s3 := Sym(54)!( 5,12)( 6, 8)( 7,23)( 9,13)(10,47)(11,15)(14,38)(16,24)(17,52)(18,46)(19,30)(20,29)(21,33)(22,27)(25,48)(26,37)(28,42)(31,51)(32,43)(34,41)(35,40)(36,45)(39,49)(44,50); s4 := Sym(54)!( 5,51)( 6,49)( 7,46)( 8,52)( 9,43)(10,41)(11,37)(12,48)(13,35)(14,28)(15,47)(16,30)(17,33)(18,42)(19,50)(20,25)(21,39)(22,24)(23,38)(26,34)(27,44)(29,31)(32,45)(36,40); s5 := Sym(54)!(53,54); poly := sub<Sym(54)|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, s4*s5*s4*s5, s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*s3, s3*s2*s3*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s2 >;