Overview
- Group
- SmallGroup(768,1076041)
- Rank
- 5
- Schläfli Type
- {2,16,6,2}
- Vertices, edges, …
- 2, 16, 48, 6, 2
- 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 := ( 9,12)(10,13)(11,14)(15,21)(16,22)(17,23)(18,24)(19,25)(20,26)(27,45)(28,46)(29,47)(30,48)(31,49)(32,50)(33,39)(34,40)(35,41)(36,42)(37,43)(38,44);; s2 := ( 3,27)( 4,29)( 5,28)( 6,30)( 7,32)( 8,31)( 9,36)(10,38)(11,37)(12,33)(13,35)(14,34)(15,45)(16,47)(17,46)(18,48)(19,50)(20,49)(21,39)(22,41)(23,40)(24,42)(25,44)(26,43);; s3 := ( 3, 4)( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)(33,34)(36,37)(39,40)(42,43)(45,46)(48,49);; s4 := (51,52);; 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,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*s2,
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(52)!(1,2); s1 := Sym(52)!( 9,12)(10,13)(11,14)(15,21)(16,22)(17,23)(18,24)(19,25)(20,26)(27,45)(28,46)(29,47)(30,48)(31,49)(32,50)(33,39)(34,40)(35,41)(36,42)(37,43)(38,44); s2 := Sym(52)!( 3,27)( 4,29)( 5,28)( 6,30)( 7,32)( 8,31)( 9,36)(10,38)(11,37)(12,33)(13,35)(14,34)(15,45)(16,47)(17,46)(18,48)(19,50)(20,49)(21,39)(22,41)(23,40)(24,42)(25,44)(26,43); s3 := Sym(52)!( 3, 4)( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)(33,34)(36,37)(39,40)(42,43)(45,46)(48,49); s4 := Sym(52)!(51,52); poly := sub<Sym(52)|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, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*s2, 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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;