Overview
- Group
- SmallGroup(1920,235343)
- Rank
- 6
- Schläfli Type
- {2,10,8,2,3}
- Vertices, edges, …
- 2, 10, 40, 8, 3, 3
- Order of s0s1s2s3s4s5
- 120
- 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
5-fold
8-fold
10-fold
20-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 7)( 5, 6)( 9,12)(10,11)(14,17)(15,16)(19,22)(20,21)(24,27)(25,26)(29,32)(30,31)(34,37)(35,36)(39,42)(40,41);; s2 := ( 3, 4)( 5, 7)( 8, 9)(10,12)(13,19)(14,18)(15,22)(16,21)(17,20)(23,39)(24,38)(25,42)(26,41)(27,40)(28,34)(29,33)(30,37)(31,36)(32,35);; s3 := ( 3,23)( 4,24)( 5,25)( 6,26)( 7,27)( 8,28)( 9,29)(10,30)(11,31)(12,32)(13,38)(14,39)(15,40)(16,41)(17,42)(18,33)(19,34)(20,35)(21,36)(22,37);; s4 := (44,45);; s5 := (43,44);; 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, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s3*s4*s3*s4, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s4*s5*s4*s5*s4*s5, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(45)!(1,2); s1 := Sym(45)!( 4, 7)( 5, 6)( 9,12)(10,11)(14,17)(15,16)(19,22)(20,21)(24,27)(25,26)(29,32)(30,31)(34,37)(35,36)(39,42)(40,41); s2 := Sym(45)!( 3, 4)( 5, 7)( 8, 9)(10,12)(13,19)(14,18)(15,22)(16,21)(17,20)(23,39)(24,38)(25,42)(26,41)(27,40)(28,34)(29,33)(30,37)(31,36)(32,35); s3 := Sym(45)!( 3,23)( 4,24)( 5,25)( 6,26)( 7,27)( 8,28)( 9,29)(10,30)(11,31)(12,32)(13,38)(14,39)(15,40)(16,41)(17,42)(18,33)(19,34)(20,35)(21,36)(22,37); s4 := Sym(45)!(44,45); s5 := Sym(45)!(43,44); poly := sub<Sym(45)|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, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5*s4*s5, s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;