Overview
- Group
- SmallGroup(864,4701)
- Rank
- 4
- Schläfli Type
- {2,6,12}
- Vertices, edges, …
- 2, 18, 108, 36
- Order of s0s1s2s3
- 12
- Order of s0s1s2s3s2s1
- 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
6-fold
9-fold
18-fold
27-fold
36-fold
54-fold
Covers minimal covers in bold
2-fold
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 3,30)( 4,31)( 5,32)( 6,36)( 7,37)( 8,38)( 9,33)(10,34)(11,35)(12,48)(13,49)(14,50)(15,54)(16,55)(17,56)(18,51)(19,52)(20,53)(21,39)(22,40)(23,41)(24,45)(25,46)(26,47)(27,42)(28,43)(29,44);; s2 := ( 3, 6)( 4, 8)( 5, 7)(10,11)(12,15)(13,17)(14,16)(19,20)(21,24)(22,26)(23,25)(28,29)(30,33)(31,35)(32,34)(37,38)(39,42)(40,44)(41,43)(46,47)(48,51)(49,53)(50,52)(55,56);; s3 := ( 3, 4)( 6,13)( 7,12)( 8,14)( 9,22)(10,21)(11,23)(15,16)(18,25)(19,24)(20,26)(27,28)(30,31)(33,40)(34,39)(35,41)(36,49)(37,48)(38,50)(42,43)(45,52)(46,51)(47,53)(54,55);; 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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s3*s2*s1*s2*s1*s3*s2*s1*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(56)!(1,2); s1 := Sym(56)!( 3,30)( 4,31)( 5,32)( 6,36)( 7,37)( 8,38)( 9,33)(10,34)(11,35)(12,48)(13,49)(14,50)(15,54)(16,55)(17,56)(18,51)(19,52)(20,53)(21,39)(22,40)(23,41)(24,45)(25,46)(26,47)(27,42)(28,43)(29,44); s2 := Sym(56)!( 3, 6)( 4, 8)( 5, 7)(10,11)(12,15)(13,17)(14,16)(19,20)(21,24)(22,26)(23,25)(28,29)(30,33)(31,35)(32,34)(37,38)(39,42)(40,44)(41,43)(46,47)(48,51)(49,53)(50,52)(55,56); s3 := Sym(56)!( 3, 4)( 6,13)( 7,12)( 8,14)( 9,22)(10,21)(11,23)(15,16)(18,25)(19,24)(20,26)(27,28)(30,31)(33,40)(34,39)(35,41)(36,49)(37,48)(38,50)(42,43)(45,52)(46,51)(47,53)(54,55); poly := sub<Sym(56)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s3*s2*s1*s2*s1*s3*s2*s1*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;