Overview
- Group
- SmallGroup(144,109)
- Rank
- 3
- Schläfli Type
- {18,4}
- Vertices, edges, …
- 18, 36, 4
- Order of s0s1s2
- 18
- Order of s0s1s2s1
- 4
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Non-Orientable
- Flat
- Self-Petrie
Quotients maximal quotients in bold
2-fold
3-fold
6-fold
Covers minimal covers in bold
2-fold
3-fold
4-fold
5-fold
6-fold
7-fold
8-fold
- {36,4}*1152b
- {36,4}*1152c
- {18,8}*1152b
- {18,8}*1152c
- {144,4}*1152c
- {144,4}*1152d
- {36,4}*1152d
- {36,8}*1152e
- {36,8}*1152f
- {18,4}*1152a
- {18,8}*1152d
- {18,8}*1152e
- {18,8}*1152f
- {36,8}*1152g
- {36,8}*1152h
- {72,4}*1152c
- {72,4}*1152d
- {18,8}*1152g
- {36,4}*1152e
- {72,4}*1152e
- {18,4}*1152b
- {72,4}*1152f
9-fold
10-fold
11-fold
12-fold
- {54,4}*1728a
- {216,4}*1728c
- {216,4}*1728d
- {108,4}*1728b
- {54,4}*1728b
- {108,4}*1728c
- {54,8}*1728b
- {54,8}*1728c
- {36,12}*1728e
- {36,12}*1728f
- {18,12}*1728c
- {36,12}*1728g
- {18,24}*1728b
- {18,24}*1728c
- {18,24}*1728d
- {18,24}*1728e
- {18,12}*1728d
- {36,12}*1728h
13-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(13,29)(14,31)(15,30)(16,32)(17,25)(18,27)(19,26)(20,28)(21,33)(22,35)(23,34)(24,36)(38,39)(41,45)(42,47)(43,46)(44,48)(49,65)(50,67)(51,66)(52,68)(53,61)(54,63)(55,62)(56,64)(57,69)(58,71)(59,70)(60,72);; s1 := ( 1,49)( 2,50)( 3,52)( 4,51)( 5,57)( 6,58)( 7,60)( 8,59)( 9,53)(10,54)(11,56)(12,55)(13,37)(14,38)(15,40)(16,39)(17,45)(18,46)(19,48)(20,47)(21,41)(22,42)(23,44)(24,43)(25,65)(26,66)(27,68)(28,67)(29,61)(30,62)(31,64)(32,63)(33,69)(34,70)(35,72)(36,71);; s2 := ( 1, 4)( 2, 3)( 5, 8)( 6, 7)( 9,12)(10,11)(13,16)(14,15)(17,20)(18,19)(21,24)(22,23)(25,28)(26,27)(29,32)(30,31)(33,36)(34,35)(37,40)(38,39)(41,44)(42,43)(45,48)(46,47)(49,52)(50,51)(53,56)(54,55)(57,60)(58,59)(61,64)(62,63)(65,68)(66,67)(69,72)(70,71);; 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,
s2*s1*s0*s2*s1*s2*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*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(72)!( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(13,29)(14,31)(15,30)(16,32)(17,25)(18,27)(19,26)(20,28)(21,33)(22,35)(23,34)(24,36)(38,39)(41,45)(42,47)(43,46)(44,48)(49,65)(50,67)(51,66)(52,68)(53,61)(54,63)(55,62)(56,64)(57,69)(58,71)(59,70)(60,72); s1 := Sym(72)!( 1,49)( 2,50)( 3,52)( 4,51)( 5,57)( 6,58)( 7,60)( 8,59)( 9,53)(10,54)(11,56)(12,55)(13,37)(14,38)(15,40)(16,39)(17,45)(18,46)(19,48)(20,47)(21,41)(22,42)(23,44)(24,43)(25,65)(26,66)(27,68)(28,67)(29,61)(30,62)(31,64)(32,63)(33,69)(34,70)(35,72)(36,71); s2 := Sym(72)!( 1, 4)( 2, 3)( 5, 8)( 6, 7)( 9,12)(10,11)(13,16)(14,15)(17,20)(18,19)(21,24)(22,23)(25,28)(26,27)(29,32)(30,31)(33,36)(34,35)(37,40)(38,39)(41,44)(42,43)(45,48)(46,47)(49,52)(50,51)(53,56)(54,55)(57,60)(58,59)(61,64)(62,63)(65,68)(66,67)(69,72)(70,71); poly := sub<Sym(72)|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, s2*s1*s0*s2*s1*s2*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*s0*s1*s0*s1 >;
References
None.
to this polytope.