Overview
- Group
- SmallGroup(1728,30173)
- Rank
- 5
- Schläfli Type
- {12,4,2,9}
- Vertices, edges, …
- 12, 24, 4, 9, 9
- Order of s0s1s2s3s4
- 36
- 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
3-fold
4-fold
6-fold
12-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 4, 5)( 6,16)( 8,12)( 9,11)(10,24)(13,29)(14,32)(15,17)(18,34)(19,20)(21,37)(22,40)(23,30)(25,28)(26,44)(27,41)(31,43)(35,46)(36,38)(39,48)(42,45);; s1 := ( 1, 8)( 2, 4)( 3,19)( 5, 9)( 6,43)( 7,11)(10,34)(12,20)(13,48)(14,42)(15,26)(16,25)(17,29)(18,23)(21,44)(22,33)(24,38)(27,47)(28,39)(30,37)(31,36)(32,41)(35,45)(40,46);; s2 := ( 1,33)( 2,42)( 3,45)( 4,34)( 5,18)( 6,16)( 7,47)( 8,43)( 9,26)(10,29)(11,44)(12,31)(13,24)(14,17)(15,32)(19,48)(20,39)(21,37)(22,25)(23,41)(27,30)(28,40)(35,38)(36,46);; s3 := (50,51)(52,53)(54,55)(56,57);; s4 := (49,50)(51,52)(53,54)(55,56);; 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,
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, s2*s1*s0*s2*s1*s2*s1*s0*s1,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
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(57)!( 2, 3)( 4, 5)( 6,16)( 8,12)( 9,11)(10,24)(13,29)(14,32)(15,17)(18,34)(19,20)(21,37)(22,40)(23,30)(25,28)(26,44)(27,41)(31,43)(35,46)(36,38)(39,48)(42,45); s1 := Sym(57)!( 1, 8)( 2, 4)( 3,19)( 5, 9)( 6,43)( 7,11)(10,34)(12,20)(13,48)(14,42)(15,26)(16,25)(17,29)(18,23)(21,44)(22,33)(24,38)(27,47)(28,39)(30,37)(31,36)(32,41)(35,45)(40,46); s2 := Sym(57)!( 1,33)( 2,42)( 3,45)( 4,34)( 5,18)( 6,16)( 7,47)( 8,43)( 9,26)(10,29)(11,44)(12,31)(13,24)(14,17)(15,32)(19,48)(20,39)(21,37)(22,25)(23,41)(27,30)(28,40)(35,38)(36,46); s3 := Sym(57)!(50,51)(52,53)(54,55)(56,57); s4 := Sym(57)!(49,50)(51,52)(53,54)(55,56); poly := sub<Sym(57)|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, 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, s2*s1*s0*s2*s1*s2*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;