Overview
- Group
- SmallGroup(576,6139)
- Rank
- 4
- Schläfli Type
- {6,4,12}
- Vertices, edges, …
- 6, 12, 24, 12
- Order of s0s1s2s3
- 12
- Order of s0s1s2s3s2s1
- 2
- Also known as
- {{6,4|2},{4,12|2}}. if this polytope has another name.
Special Properties
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
8-fold
9-fold
12-fold
16-fold
18-fold
24-fold
36-fold
Covers minimal covers in bold
2-fold
3-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(32,33)(35,36)(38,39)(41,42)(44,45)(47,48)(50,51)(53,54)(56,57)(59,60)(62,63)(65,66)(68,69)(71,72);; s1 := ( 1, 2)( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)(34,35)(37,47)(38,46)(39,48)(40,50)(41,49)(42,51)(43,53)(44,52)(45,54)(55,65)(56,64)(57,66)(58,68)(59,67)(60,69)(61,71)(62,70)(63,72);; s2 := ( 1,37)( 2,38)( 3,39)( 4,43)( 5,44)( 6,45)( 7,40)( 8,41)( 9,42)(10,46)(11,47)(12,48)(13,52)(14,53)(15,54)(16,49)(17,50)(18,51)(19,55)(20,56)(21,57)(22,61)(23,62)(24,63)(25,58)(26,59)(27,60)(28,64)(29,65)(30,66)(31,70)(32,71)(33,72)(34,67)(35,68)(36,69);; s3 := ( 1, 4)( 2, 5)( 3, 6)(10,13)(11,14)(12,15)(19,22)(20,23)(21,24)(28,31)(29,32)(30,33)(37,58)(38,59)(39,60)(40,55)(41,56)(42,57)(43,61)(44,62)(45,63)(46,67)(47,68)(48,69)(49,64)(50,65)(51,66)(52,70)(53,71)(54,72);; 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, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
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(72)!( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(32,33)(35,36)(38,39)(41,42)(44,45)(47,48)(50,51)(53,54)(56,57)(59,60)(62,63)(65,66)(68,69)(71,72); s1 := Sym(72)!( 1, 2)( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)(34,35)(37,47)(38,46)(39,48)(40,50)(41,49)(42,51)(43,53)(44,52)(45,54)(55,65)(56,64)(57,66)(58,68)(59,67)(60,69)(61,71)(62,70)(63,72); s2 := Sym(72)!( 1,37)( 2,38)( 3,39)( 4,43)( 5,44)( 6,45)( 7,40)( 8,41)( 9,42)(10,46)(11,47)(12,48)(13,52)(14,53)(15,54)(16,49)(17,50)(18,51)(19,55)(20,56)(21,57)(22,61)(23,62)(24,63)(25,58)(26,59)(27,60)(28,64)(29,65)(30,66)(31,70)(32,71)(33,72)(34,67)(35,68)(36,69); s3 := Sym(72)!( 1, 4)( 2, 5)( 3, 6)(10,13)(11,14)(12,15)(19,22)(20,23)(21,24)(28,31)(29,32)(30,33)(37,58)(38,59)(39,60)(40,55)(41,56)(42,57)(43,61)(44,62)(45,63)(46,67)(47,68)(48,69)(49,64)(50,65)(51,66)(52,70)(53,71)(54,72); poly := sub<Sym(72)|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, s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References
None.
to this polytope.