Overview
- Group
- SmallGroup(144,109)
- Rank
- 3
- Schläfli Type
- {4,18}
- Vertices, edges, …
- 4, 36, 18
- 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
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
- {4,36}*1152b
- {4,36}*1152c
- {8,18}*1152b
- {8,18}*1152c
- {4,144}*1152c
- {4,144}*1152d
- {4,36}*1152d
- {8,36}*1152e
- {8,36}*1152f
- {4,18}*1152a
- {8,18}*1152d
- {8,18}*1152e
- {8,18}*1152f
- {8,36}*1152g
- {8,36}*1152h
- {4,72}*1152c
- {4,72}*1152d
- {8,18}*1152g
- {4,36}*1152e
- {4,72}*1152e
- {4,18}*1152b
- {4,72}*1152f
9-fold
10-fold
11-fold
12-fold
- {4,54}*1728a
- {4,216}*1728c
- {4,216}*1728d
- {4,108}*1728b
- {4,54}*1728b
- {4,108}*1728c
- {8,54}*1728b
- {8,54}*1728c
- {12,36}*1728e
- {12,36}*1728f
- {12,18}*1728c
- {12,36}*1728g
- {24,18}*1728b
- {24,18}*1728c
- {24,18}*1728d
- {24,18}*1728e
- {12,18}*1728d
- {12,36}*1728h
13-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60)(61,62)(63,64)(65,66)(67,68)(69,70)(71,72);; s1 := ( 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);; s2 := ( 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);; 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*s2*s1*s0*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(72)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60)(61,62)(63,64)(65,66)(67,68)(69,70)(71,72); s1 := 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); s2 := 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); 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, s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*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.