Overview
- Group
- SmallGroup(1944,2346)
- Rank
- 3
- Schläfli Type
- {18,6}
- Vertices, edges, …
- 162, 486, 54
- Order of s0s1s2
- 6
- Order of s0s1s2s1
- 18
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
3-fold
6-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*s2*(s1*s0)^2*(s2*s1)^2*s0*s1*s2> of order 3
18 facets
- 18 of {18}*36
54 vertex figures
- 54 of {6}*12
P/N, where N=<(s0*s1)^3*s0*s2*(s1*s0)^2*s1*s2> of order 3
18 facets
- 18 of {18}*36
54 vertex figures
- 54 of {6}*12
P/N, where N=<s1*s0*s1*s2*(s1*s0)^3*s1*s2> of order 3
18 facets
- 18 of {18}*36
54 vertex figures
- 54 of {6}*12
P/N, where N=<(s0*s1)^4*s0*(s2*s1)^2*s0*(s1*s2)^2> of order 3
18 facets
- 18 of {18}*36
54 vertex figures
- 54 of {6}*12
P/N, where N=<s0*(s1*s2)^2*(s1*s0)^2*s2*s1*s2, (s0*s2*s1)^2*s0*(s1*s2)^2*s1> of order 6
12 facets
27 vertex figures
- 27 of {6}*12
P/N, where N=<(s0*s1)^2*(s2*s1)^2*s0*s2*s1*s2, (s0*s1)^3*s0*s2*(s1*s0)^2*s1*s2> of order 6
12 facets
27 vertex figures
- 27 of {6}*12
P/N, where N=<s1*s0*(s1*s2)^2*s1*s0*s2*s1, s0*s1*s2*(s1*s0)^3*s2*s1*s2> of order 6
9 facets
- 9 of {18}*36
36 vertex figures
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 4, 7)( 5, 9)( 6, 8)(10,20)(11,19)(12,21)(13,26)(14,25)(15,27)(16,23)(17,22)(18,24)(28,55)(29,57)(30,56)(31,61)(32,63)(33,62)(34,58)(35,60)(36,59)(37,74)(38,73)(39,75)(40,80)(41,79)(42,81)(43,77)(44,76)(45,78)(46,65)(47,64)(48,66)(49,71)(50,70)(51,72)(52,68)(53,67)(54,69);; s1 := ( 1,37)( 2,39)( 3,38)( 4,40)( 5,42)( 6,41)( 7,43)( 8,45)( 9,44)(10,28)(11,30)(12,29)(13,31)(14,33)(15,32)(16,34)(17,36)(18,35)(19,47)(20,46)(21,48)(22,50)(23,49)(24,51)(25,53)(26,52)(27,54)(55,64)(56,66)(57,65)(58,67)(59,69)(60,68)(61,70)(62,72)(63,71)(73,74)(76,77)(79,80);; s2 := ( 2, 3)( 4, 5)( 7, 9)(10,27)(11,26)(12,25)(13,19)(14,21)(15,20)(16,23)(17,22)(18,24)(29,30)(31,32)(34,36)(37,54)(38,53)(39,52)(40,46)(41,48)(42,47)(43,50)(44,49)(45,51)(56,57)(58,59)(61,63)(64,81)(65,80)(66,79)(67,73)(68,75)(69,74)(70,77)(71,76)(72,78);; 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(81)!( 2, 3)( 4, 7)( 5, 9)( 6, 8)(10,20)(11,19)(12,21)(13,26)(14,25)(15,27)(16,23)(17,22)(18,24)(28,55)(29,57)(30,56)(31,61)(32,63)(33,62)(34,58)(35,60)(36,59)(37,74)(38,73)(39,75)(40,80)(41,79)(42,81)(43,77)(44,76)(45,78)(46,65)(47,64)(48,66)(49,71)(50,70)(51,72)(52,68)(53,67)(54,69); s1 := Sym(81)!( 1,37)( 2,39)( 3,38)( 4,40)( 5,42)( 6,41)( 7,43)( 8,45)( 9,44)(10,28)(11,30)(12,29)(13,31)(14,33)(15,32)(16,34)(17,36)(18,35)(19,47)(20,46)(21,48)(22,50)(23,49)(24,51)(25,53)(26,52)(27,54)(55,64)(56,66)(57,65)(58,67)(59,69)(60,68)(61,70)(62,72)(63,71)(73,74)(76,77)(79,80); s2 := Sym(81)!( 2, 3)( 4, 5)( 7, 9)(10,27)(11,26)(12,25)(13,19)(14,21)(15,20)(16,23)(17,22)(18,24)(29,30)(31,32)(34,36)(37,54)(38,53)(39,52)(40,46)(41,48)(42,47)(43,50)(44,49)(45,51)(56,57)(58,59)(61,63)(64,81)(65,80)(66,79)(67,73)(68,75)(69,74)(70,77)(71,76)(72,78); 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1 >;
References
None.
to this polytope.