Overview
- Group
- SmallGroup(1944,944)
- Rank
- 4
- Schläfli Type
- {2,9,6}
- Vertices, edges, …
- 2, 81, 243, 54
- Order of s0s1s2s3
- 18
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
3-fold
9-fold
27-fold
81-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 5)( 6, 9)( 7,11)( 8,10)(12,20)(13,19)(14,18)(15,17)(21,25)(22,24)(23,26)(27,28)(30,58)(31,57)(32,59)(33,64)(34,63)(35,65)(36,61)(37,60)(38,62)(39,72)(40,74)(41,73)(42,69)(43,71)(44,70)(45,66)(46,68)(47,67)(48,80)(49,79)(50,78)(51,77)(52,76)(53,75)(54,83)(55,82)(56,81);; s2 := ( 3,39)( 4,41)( 5,40)( 6,45)( 7,47)( 8,46)( 9,42)(10,44)(11,43)(12,49)(13,48)(14,50)(15,55)(16,54)(17,56)(18,52)(19,51)(20,53)(21,32)(22,31)(23,30)(24,38)(25,37)(26,36)(27,35)(28,34)(29,33)(57,65)(58,64)(59,63)(60,62)(66,72)(67,74)(68,73)(70,71)(75,82)(76,81)(77,83)(78,79);; s3 := ( 6, 9)( 7,10)( 8,11)(12,22)(13,23)(14,21)(15,28)(16,29)(17,27)(18,25)(19,26)(20,24)(33,36)(34,37)(35,38)(39,49)(40,50)(41,48)(42,55)(43,56)(44,54)(45,52)(46,53)(47,51)(60,63)(61,64)(62,65)(66,76)(67,77)(68,75)(69,82)(70,83)(71,81)(72,79)(73,80)(74,78);; 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,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s3*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(83)!(1,2); s1 := Sym(83)!( 4, 5)( 6, 9)( 7,11)( 8,10)(12,20)(13,19)(14,18)(15,17)(21,25)(22,24)(23,26)(27,28)(30,58)(31,57)(32,59)(33,64)(34,63)(35,65)(36,61)(37,60)(38,62)(39,72)(40,74)(41,73)(42,69)(43,71)(44,70)(45,66)(46,68)(47,67)(48,80)(49,79)(50,78)(51,77)(52,76)(53,75)(54,83)(55,82)(56,81); s2 := Sym(83)!( 3,39)( 4,41)( 5,40)( 6,45)( 7,47)( 8,46)( 9,42)(10,44)(11,43)(12,49)(13,48)(14,50)(15,55)(16,54)(17,56)(18,52)(19,51)(20,53)(21,32)(22,31)(23,30)(24,38)(25,37)(26,36)(27,35)(28,34)(29,33)(57,65)(58,64)(59,63)(60,62)(66,72)(67,74)(68,73)(70,71)(75,82)(76,81)(77,83)(78,79); s3 := Sym(83)!( 6, 9)( 7,10)( 8,11)(12,22)(13,23)(14,21)(15,28)(16,29)(17,27)(18,25)(19,26)(20,24)(33,36)(34,37)(35,38)(39,49)(40,50)(41,48)(42,55)(43,56)(44,54)(45,52)(46,53)(47,51)(60,63)(61,64)(62,65)(66,76)(67,77)(68,75)(69,82)(70,83)(71,81)(72,79)(73,80)(74,78); poly := sub<Sym(83)|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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s3*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2 >;