Overview
- Group
- SmallGroup(216,101)
- Rank
- 3
- Schläfli Type
- {18,6}
- Vertices, edges, …
- 18, 54, 6
- Order of s0s1s2
- 18
- Order of s0s1s2s1
- 2
- Also known as
- {18,6|2}. if this polytope has another name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Flat
Quotients maximal quotients in bold
3-fold
6-fold
9-fold
18-fold
27-fold
Covers minimal covers in bold
2-fold
3-fold
4-fold
5-fold
6-fold
- {18,36}*1296a
- {36,18}*1296a
- {18,12}*1296a
- {36,6}*1296b
- {54,12}*1296a
- {108,6}*1296a
- {36,6}*1296l
- {18,12}*1296l
7-fold
8-fold
- {144,6}*1728a
- {18,48}*1728a
- {36,12}*1728a
- {72,12}*1728a
- {36,24}*1728c
- {72,12}*1728c
- {36,24}*1728d
- {36,12}*1728c
- {36,6}*1728b
- {72,6}*1728b
- {72,6}*1728c
- {36,12}*1728d
- {36,12}*1728e
- {18,12}*1728c
- {18,24}*1728c
- {18,24}*1728e
- {36,12}*1728h
9-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 5, 6)( 8, 9)(10,20)(11,19)(12,21)(13,23)(14,22)(15,24)(16,26)(17,25)(18,27)(29,30)(32,33)(35,36)(37,47)(38,46)(39,48)(40,50)(41,49)(42,51)(43,53)(44,52)(45,54);; s1 := ( 1,10)( 2,12)( 3,11)( 4,16)( 5,18)( 6,17)( 7,13)( 8,15)( 9,14)(19,20)(22,26)(23,25)(24,27)(28,37)(29,39)(30,38)(31,43)(32,45)(33,44)(34,40)(35,42)(36,41)(46,47)(49,53)(50,52)(51,54);; s2 := ( 1,31)( 2,32)( 3,33)( 4,28)( 5,29)( 6,30)( 7,34)( 8,35)( 9,36)(10,40)(11,41)(12,42)(13,37)(14,38)(15,39)(16,43)(17,44)(18,45)(19,49)(20,50)(21,51)(22,46)(23,47)(24,48)(25,52)(26,53)(27,54);; 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*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(54)!( 2, 3)( 5, 6)( 8, 9)(10,20)(11,19)(12,21)(13,23)(14,22)(15,24)(16,26)(17,25)(18,27)(29,30)(32,33)(35,36)(37,47)(38,46)(39,48)(40,50)(41,49)(42,51)(43,53)(44,52)(45,54); s1 := Sym(54)!( 1,10)( 2,12)( 3,11)( 4,16)( 5,18)( 6,17)( 7,13)( 8,15)( 9,14)(19,20)(22,26)(23,25)(24,27)(28,37)(29,39)(30,38)(31,43)(32,45)(33,44)(34,40)(35,42)(36,41)(46,47)(49,53)(50,52)(51,54); s2 := Sym(54)!( 1,31)( 2,32)( 3,33)( 4,28)( 5,29)( 6,30)( 7,34)( 8,35)( 9,36)(10,40)(11,41)(12,42)(13,37)(14,38)(15,39)(16,43)(17,44)(18,45)(19,49)(20,50)(21,51)(22,46)(23,47)(24,48)(25,52)(26,53)(27,54); poly := sub<Sym(54)|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*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References
None.
to this polytope.