Overview
- Group
- SmallGroup(1944,2341)
- Rank
- 3
- Schläfli Type
- {6,18}
- Vertices, edges, …
- 54, 486, 162
- Order of s0s1s2
- 18
- Order of s0s1s2s1
- 6
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
3-fold
9-fold
18-fold
27-fold
54-fold
81-fold
162-fold
243-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
Click an entry to reveal its facets and vertex figures.
P/N, where N=<s0*s1*s0*s2*(s1*s0)^2*s2*s1> of order 3
54 facets
- 54 of {6}*12
18 vertex figures
- 18 of {18}*36
P/N, where N=<s0*(s1*s2)^3*s1*s0*(s2*s1)^2*s2> of order 3
54 facets
- 54 of {6}*12
18 vertex figures
- 18 of {18}*36
P/N, where N=<(s0*s1)^2*(s2*s1*s0)^2*(s2*s1)^4> of order 3
54 facets
- 54 of {6}*12
18 vertex figures
- 18 of {18}*36
P/N, where N=<s0*s1*s0*s2*(s1*s0)^2*s2*s1, (s1*s2)^9> of order 6
27 facets
- 27 of {6}*12
12 vertex figures
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 := ( 1,29)( 2,30)( 3,28)( 4,35)( 5,36)( 6,34)( 7,32)( 8,33)( 9,31)(10,50)(11,51)(12,49)(13,47)(14,48)(15,46)(16,53)(17,54)(18,52)(19,41)(20,42)(21,40)(22,38)(23,39)(24,37)(25,44)(26,45)(27,43)(58,61)(59,62)(60,63)(64,76)(65,77)(66,78)(67,73)(68,74)(69,75)(70,79)(71,80)(72,81);; s2 := ( 1,10)( 2,12)( 3,11)( 4,16)( 5,18)( 6,17)( 7,13)( 8,15)( 9,14)(19,22)(20,24)(21,23)(26,27)(28,37)(29,39)(30,38)(31,43)(32,45)(33,44)(34,40)(35,42)(36,41)(46,49)(47,51)(48,50)(53,54)(55,64)(56,66)(57,65)(58,70)(59,72)(60,71)(61,67)(62,69)(63,68)(73,76)(74,78)(75,77)(80,81);; poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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(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)!( 1,29)( 2,30)( 3,28)( 4,35)( 5,36)( 6,34)( 7,32)( 8,33)( 9,31)(10,50)(11,51)(12,49)(13,47)(14,48)(15,46)(16,53)(17,54)(18,52)(19,41)(20,42)(21,40)(22,38)(23,39)(24,37)(25,44)(26,45)(27,43)(58,61)(59,62)(60,63)(64,76)(65,77)(66,78)(67,73)(68,74)(69,75)(70,79)(71,80)(72,81); s2 := Sym(81)!( 1,10)( 2,12)( 3,11)( 4,16)( 5,18)( 6,17)( 7,13)( 8,15)( 9,14)(19,22)(20,24)(21,23)(26,27)(28,37)(29,39)(30,38)(31,43)(32,45)(33,44)(34,40)(35,42)(36,41)(46,49)(47,51)(48,50)(53,54)(55,64)(56,66)(57,65)(58,70)(59,72)(60,71)(61,67)(62,69)(63,68)(73,76)(74,78)(75,77)(80,81); poly := sub<Sym(81)|s0,s1,s2>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References
None.
to this polytope.