Overview
- Group
- SmallGroup(1920,203905)
- Rank
- 5
- Schläfli Type
- {2,5,2,48}
- Vertices, edges, …
- 2, 5, 5, 48, 48
- Order of s0s1s2s3s4
- 240
- Order of s0s1s2s3s4s3s2s1
- 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
6-fold
8-fold
12-fold
16-fold
24-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := (4,5)(6,7);; s2 := (3,4)(5,6);; s3 := ( 9,10)(11,12)(13,16)(14,18)(15,17)(19,22)(20,24)(21,23)(25,28)(26,30)(27,29)(31,34)(32,36)(33,35)(37,40)(38,42)(39,41)(43,46)(44,48)(45,47)(50,53)(51,52)(54,55);; s4 := ( 8,14)( 9,11)(10,20)(12,15)(13,17)(16,26)(18,21)(19,23)(22,32)(24,27)(25,29)(28,38)(30,33)(31,35)(34,44)(36,39)(37,41)(40,50)(42,45)(43,47)(46,54)(48,51)(49,52)(53,55);; 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*s1*s0*s1,
s0*s2*s0*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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
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*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*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*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(55)!(1,2); s1 := Sym(55)!(4,5)(6,7); s2 := Sym(55)!(3,4)(5,6); s3 := Sym(55)!( 9,10)(11,12)(13,16)(14,18)(15,17)(19,22)(20,24)(21,23)(25,28)(26,30)(27,29)(31,34)(32,36)(33,35)(37,40)(38,42)(39,41)(43,46)(44,48)(45,47)(50,53)(51,52)(54,55); s4 := Sym(55)!( 8,14)( 9,11)(10,20)(12,15)(13,17)(16,26)(18,21)(19,23)(22,32)(24,27)(25,29)(28,38)(30,33)(31,35)(34,44)(36,39)(37,41)(40,50)(42,45)(43,47)(46,54)(48,51)(49,52)(53,55); poly := sub<Sym(55)|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*s1*s0*s1, s0*s2*s0*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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 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*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*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*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;