Overview
- Group
- SmallGroup(1920,238620)
- Rank
- 5
- Schläfli Type
- {40,2,4,3}
- Vertices, edges, …
- 40, 40, 4, 6, 3
- Order of s0s1s2s3s4
- 120
- Order of s0s1s2s3s4s3s2s1
- 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
5-fold
8-fold
10-fold
20-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 4, 5)( 6, 9)( 7,11)( 8,10)(12,13)(14,19)(15,21)(16,20)(17,23)(18,22)(25,30)(26,29)(27,32)(28,31)(33,34)(35,38)(36,37)(39,40);; s1 := ( 1, 7)( 2, 4)( 3,15)( 5,17)( 6,10)( 8,12)( 9,25)(11,27)(13,18)(14,20)(16,22)(19,33)(21,35)(23,28)(24,29)(26,31)(30,39)(32,36)(34,37)(38,40);; s2 := (41,42)(43,44);; s3 := (42,43);; s4 := (43,44);; poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, 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,
s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3,
s4*s2*s3*s4*s2*s3*s4*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(44)!( 2, 3)( 4, 5)( 6, 9)( 7,11)( 8,10)(12,13)(14,19)(15,21)(16,20)(17,23)(18,22)(25,30)(26,29)(27,32)(28,31)(33,34)(35,38)(36,37)(39,40); s1 := Sym(44)!( 1, 7)( 2, 4)( 3,15)( 5,17)( 6,10)( 8,12)( 9,25)(11,27)(13,18)(14,20)(16,22)(19,33)(21,35)(23,28)(24,29)(26,31)(30,39)(32,36)(34,37)(38,40); s2 := Sym(44)!(41,42)(43,44); s3 := Sym(44)!(42,43); s4 := Sym(44)!(43,44); poly := sub<Sym(44)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, 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, s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3, s4*s2*s3*s4*s2*s3*s4*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;