Overview
- Group
- SmallGroup(768,1076043)
- Rank
- 5
- Schläfli Type
- {2,2,2,48}
- Vertices, edges, …
- 2, 2, 2, 48, 48
- Order of s0s1s2s3s4
- 48
- 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 := (3,4);; s2 := (5,6);; s3 := ( 8, 9)(10,11)(12,15)(13,17)(14,16)(18,21)(19,23)(20,22)(24,27)(25,29)(26,28)(30,33)(31,35)(32,34)(36,39)(37,41)(38,40)(42,45)(43,47)(44,46)(49,52)(50,51)(53,54);; s4 := ( 7,13)( 8,10)( 9,19)(11,14)(12,16)(15,25)(17,20)(18,22)(21,31)(23,26)(24,28)(27,37)(29,32)(30,34)(33,43)(35,38)(36,40)(39,49)(41,44)(42,46)(45,53)(47,50)(48,51)(52,54);; 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, 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, 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(54)!(1,2); s1 := Sym(54)!(3,4); s2 := Sym(54)!(5,6); s3 := Sym(54)!( 8, 9)(10,11)(12,15)(13,17)(14,16)(18,21)(19,23)(20,22)(24,27)(25,29)(26,28)(30,33)(31,35)(32,34)(36,39)(37,41)(38,40)(42,45)(43,47)(44,46)(49,52)(50,51)(53,54); s4 := Sym(54)!( 7,13)( 8,10)( 9,19)(11,14)(12,16)(15,25)(17,20)(18,22)(21,31)(23,26)(24,28)(27,37)(29,32)(30,34)(33,43)(35,38)(36,40)(39,49)(41,44)(42,46)(45,53)(47,50)(48,51)(52,54); poly := sub<Sym(54)|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, 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, 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 >;