Overview
- Group
- SmallGroup(576,1572)
- Rank
- 4
- Schläfli Type
- {18,4,4}
- Vertices, edges, …
- 18, 36, 8, 4
- Order of s0s1s2s3
- 36
- Order of s0s1s2s3s2s1
- 2
- Also known as
- {{18,4|2},{4,4|2}}. if this polytope has another name.
Special Properties
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
8-fold
9-fold
12-fold
18-fold
24-fold
36-fold
Covers minimal covers in bold
2-fold
3-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 4, 9)( 5, 8)( 6, 7)(11,12)(13,18)(14,17)(15,16)(20,21)(22,27)(23,26)(24,25)(29,30)(31,36)(32,35)(33,34)(38,39)(40,45)(41,44)(42,43)(47,48)(49,54)(50,53)(51,52)(56,57)(58,63)(59,62)(60,61)(65,66)(67,72)(68,71)(69,70);; s1 := ( 1, 4)( 2, 6)( 3, 5)( 7, 9)(10,13)(11,15)(12,14)(16,18)(19,22)(20,24)(21,23)(25,27)(28,31)(29,33)(30,32)(34,36)(37,49)(38,51)(39,50)(40,46)(41,48)(42,47)(43,54)(44,53)(45,52)(55,67)(56,69)(57,68)(58,64)(59,66)(60,65)(61,72)(62,71)(63,70);; s2 := ( 1,37)( 2,38)( 3,39)( 4,40)( 5,41)( 6,42)( 7,43)( 8,44)( 9,45)(10,46)(11,47)(12,48)(13,49)(14,50)(15,51)(16,52)(17,53)(18,54)(19,55)(20,56)(21,57)(22,58)(23,59)(24,60)(25,61)(26,62)(27,63)(28,64)(29,65)(30,66)(31,67)(32,68)(33,69)(34,70)(35,71)(36,72);; s3 := (37,55)(38,56)(39,57)(40,58)(41,59)(42,60)(43,61)(44,62)(45,63)(46,64)(47,65)(48,66)(49,67)(50,68)(51,69)(52,70)(53,71)(54,72);; poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, 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)( 4, 9)( 5, 8)( 6, 7)(11,12)(13,18)(14,17)(15,16)(20,21)(22,27)(23,26)(24,25)(29,30)(31,36)(32,35)(33,34)(38,39)(40,45)(41,44)(42,43)(47,48)(49,54)(50,53)(51,52)(56,57)(58,63)(59,62)(60,61)(65,66)(67,72)(68,71)(69,70); s1 := Sym(72)!( 1, 4)( 2, 6)( 3, 5)( 7, 9)(10,13)(11,15)(12,14)(16,18)(19,22)(20,24)(21,23)(25,27)(28,31)(29,33)(30,32)(34,36)(37,49)(38,51)(39,50)(40,46)(41,48)(42,47)(43,54)(44,53)(45,52)(55,67)(56,69)(57,68)(58,64)(59,66)(60,65)(61,72)(62,71)(63,70); s2 := Sym(72)!( 1,37)( 2,38)( 3,39)( 4,40)( 5,41)( 6,42)( 7,43)( 8,44)( 9,45)(10,46)(11,47)(12,48)(13,49)(14,50)(15,51)(16,52)(17,53)(18,54)(19,55)(20,56)(21,57)(22,58)(23,59)(24,60)(25,61)(26,62)(27,63)(28,64)(29,65)(30,66)(31,67)(32,68)(33,69)(34,70)(35,71)(36,72); s3 := Sym(72)!(37,55)(38,56)(39,57)(40,58)(41,59)(42,60)(43,61)(44,62)(45,63)(46,64)(47,65)(48,66)(49,67)(50,68)(51,69)(52,70)(53,71)(54,72); poly := sub<Sym(72)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 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.