Overview
- Group
- SmallGroup(1944,2340)
- Rank
- 4
- Schläfli Type
- {6,18,6}
- Vertices, edges, …
- 6, 81, 81, 9
- Order of s0s1s2s3
- 18
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
3-fold
9-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := (28,55)(29,56)(30,57)(31,58)(32,59)(33,60)(34,61)(35,62)(36,63)(37,64)(38,65)(39,66)(40,67)(41,68)(42,69)(43,70)(44,71)(45,72)(46,73)(47,74)(48,75)(49,76)(50,77)(51,78)(52,79)(53,80)(54,81);; s1 := ( 1,28)( 2,30)( 3,29)( 4,34)( 5,36)( 6,35)( 7,31)( 8,33)( 9,32)(10,49)(11,51)(12,50)(13,46)(14,48)(15,47)(16,52)(17,54)(18,53)(19,40)(20,42)(21,41)(22,37)(23,39)(24,38)(25,43)(26,45)(27,44)(56,57)(58,61)(59,63)(60,62)(64,76)(65,78)(66,77)(67,73)(68,75)(69,74)(70,79)(71,81)(72,80);; s2 := ( 1,10)( 2,11)( 3,12)( 4,16)( 5,17)( 6,18)( 7,13)( 8,14)( 9,15)(19,22)(20,23)(21,24)(28,64)(29,65)(30,66)(31,70)(32,71)(33,72)(34,67)(35,68)(36,69)(37,55)(38,56)(39,57)(40,61)(41,62)(42,63)(43,58)(44,59)(45,60)(46,76)(47,77)(48,78)(49,73)(50,74)(51,75)(52,79)(53,80)(54,81);; s3 := ( 2, 3)( 5, 6)( 8, 9)(10,11)(13,14)(16,17)(19,21)(22,24)(25,27)(29,30)(32,33)(35,36)(37,38)(40,41)(43,44)(46,48)(49,51)(52,54)(56,57)(59,60)(62,63)(64,65)(67,68)(70,71)(73,75)(76,78)(79,81);; 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*s0*s1*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(81)!(28,55)(29,56)(30,57)(31,58)(32,59)(33,60)(34,61)(35,62)(36,63)(37,64)(38,65)(39,66)(40,67)(41,68)(42,69)(43,70)(44,71)(45,72)(46,73)(47,74)(48,75)(49,76)(50,77)(51,78)(52,79)(53,80)(54,81); s1 := Sym(81)!( 1,28)( 2,30)( 3,29)( 4,34)( 5,36)( 6,35)( 7,31)( 8,33)( 9,32)(10,49)(11,51)(12,50)(13,46)(14,48)(15,47)(16,52)(17,54)(18,53)(19,40)(20,42)(21,41)(22,37)(23,39)(24,38)(25,43)(26,45)(27,44)(56,57)(58,61)(59,63)(60,62)(64,76)(65,78)(66,77)(67,73)(68,75)(69,74)(70,79)(71,81)(72,80); s2 := Sym(81)!( 1,10)( 2,11)( 3,12)( 4,16)( 5,17)( 6,18)( 7,13)( 8,14)( 9,15)(19,22)(20,23)(21,24)(28,64)(29,65)(30,66)(31,70)(32,71)(33,72)(34,67)(35,68)(36,69)(37,55)(38,56)(39,57)(40,61)(41,62)(42,63)(43,58)(44,59)(45,60)(46,76)(47,77)(48,78)(49,73)(50,74)(51,75)(52,79)(53,80)(54,81); s3 := Sym(81)!( 2, 3)( 5, 6)( 8, 9)(10,11)(13,14)(16,17)(19,21)(22,24)(25,27)(29,30)(32,33)(35,36)(37,38)(40,41)(43,44)(46,48)(49,51)(52,54)(56,57)(59,60)(62,63)(64,65)(67,68)(70,71)(73,75)(76,78)(79,81); poly := sub<Sym(81)|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*s0*s1*s0*s1*s2*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s1*s2 >;
References
None.
to this polytope.