Overview
- Group
- SmallGroup(1440,5900)
- Rank
- 4
- Schläfli Type
- {12,30,2}
- Vertices, edges, …
- 12, 180, 30, 2
- Order of s0s1s2s3
- 30
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
3-fold
5-fold
6-fold
15-fold
30-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16)(17,19)(18,20)(21,43)(22,44)(23,41)(24,42)(25,47)(26,48)(27,45)(28,46)(29,51)(30,52)(31,49)(32,50)(33,55)(34,56)(35,53)(36,54)(37,59)(38,60)(39,57)(40,58);; s1 := ( 1,21)( 2,23)( 3,22)( 4,24)( 5,37)( 6,39)( 7,38)( 8,40)( 9,33)(10,35)(11,34)(12,36)(13,29)(14,31)(15,30)(16,32)(17,25)(18,27)(19,26)(20,28)(42,43)(45,57)(46,59)(47,58)(48,60)(49,53)(50,55)(51,54)(52,56);; s2 := ( 1, 5)( 2, 8)( 3, 7)( 4, 6)( 9,17)(10,20)(11,19)(12,18)(14,16)(21,25)(22,28)(23,27)(24,26)(29,37)(30,40)(31,39)(32,38)(34,36)(41,45)(42,48)(43,47)(44,46)(49,57)(50,60)(51,59)(52,58)(54,56);; s3 := (61,62);; poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*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(62)!( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16)(17,19)(18,20)(21,43)(22,44)(23,41)(24,42)(25,47)(26,48)(27,45)(28,46)(29,51)(30,52)(31,49)(32,50)(33,55)(34,56)(35,53)(36,54)(37,59)(38,60)(39,57)(40,58); s1 := Sym(62)!( 1,21)( 2,23)( 3,22)( 4,24)( 5,37)( 6,39)( 7,38)( 8,40)( 9,33)(10,35)(11,34)(12,36)(13,29)(14,31)(15,30)(16,32)(17,25)(18,27)(19,26)(20,28)(42,43)(45,57)(46,59)(47,58)(48,60)(49,53)(50,55)(51,54)(52,56); s2 := Sym(62)!( 1, 5)( 2, 8)( 3, 7)( 4, 6)( 9,17)(10,20)(11,19)(12,18)(14,16)(21,25)(22,28)(23,27)(24,26)(29,37)(30,40)(31,39)(32,38)(34,36)(41,45)(42,48)(43,47)(44,46)(49,57)(50,60)(51,59)(52,58)(54,56); s3 := Sym(62)!(61,62); poly := sub<Sym(62)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;