Polytope of Type {2,18,10,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,18,10,2}*1440
if this polytope has a name.
Group : SmallGroup(1440,4583)
Rank : 5
Schlafli Type : {2,18,10,2}
Number of vertices, edges, etc : 2, 18, 90, 10, 2
Order of s0s1s2s3s4 : 90
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {2,6,10,2}*480
5-fold quotients : {2,18,2,2}*288
9-fold quotients : {2,2,10,2}*160
10-fold quotients : {2,9,2,2}*144
15-fold quotients : {2,6,2,2}*96
18-fold quotients : {2,2,5,2}*80
30-fold quotients : {2,3,2,2}*48
45-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(18,34)(19,33)(20,35)(21,37)(22,36)
(23,38)(24,40)(25,39)(26,41)(27,43)(28,42)(29,44)(30,46)(31,45)(32,47)(49,50)
(52,53)(55,56)(58,59)(61,62)(63,79)(64,78)(65,80)(66,82)(67,81)(68,83)(69,85)
(70,84)(71,86)(72,88)(73,87)(74,89)(75,91)(76,90)(77,92);;
s2 := ( 3,18)( 4,20)( 5,19)( 6,30)( 7,32)( 8,31)( 9,27)(10,29)(11,28)(12,24)
(13,26)(14,25)(15,21)(16,23)(17,22)(33,34)(36,46)(37,45)(38,47)(39,43)(40,42)
(41,44)(48,63)(49,65)(50,64)(51,75)(52,77)(53,76)(54,72)(55,74)(56,73)(57,69)
(58,71)(59,70)(60,66)(61,68)(62,67)(78,79)(81,91)(82,90)(83,92)(84,88)(85,87)
(86,89);;
s3 := ( 3,51)( 4,52)( 5,53)( 6,48)( 7,49)( 8,50)( 9,60)(10,61)(11,62)(12,57)
(13,58)(14,59)(15,54)(16,55)(17,56)(18,66)(19,67)(20,68)(21,63)(22,64)(23,65)
(24,75)(25,76)(26,77)(27,72)(28,73)(29,74)(30,69)(31,70)(32,71)(33,81)(34,82)
(35,83)(36,78)(37,79)(38,80)(39,90)(40,91)(41,92)(42,87)(43,88)(44,89)(45,84)
(46,85)(47,86);;
s4 := (93,94);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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(94)!(1,2);
s1 := Sym(94)!( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(18,34)(19,33)(20,35)(21,37)
(22,36)(23,38)(24,40)(25,39)(26,41)(27,43)(28,42)(29,44)(30,46)(31,45)(32,47)
(49,50)(52,53)(55,56)(58,59)(61,62)(63,79)(64,78)(65,80)(66,82)(67,81)(68,83)
(69,85)(70,84)(71,86)(72,88)(73,87)(74,89)(75,91)(76,90)(77,92);
s2 := Sym(94)!( 3,18)( 4,20)( 5,19)( 6,30)( 7,32)( 8,31)( 9,27)(10,29)(11,28)
(12,24)(13,26)(14,25)(15,21)(16,23)(17,22)(33,34)(36,46)(37,45)(38,47)(39,43)
(40,42)(41,44)(48,63)(49,65)(50,64)(51,75)(52,77)(53,76)(54,72)(55,74)(56,73)
(57,69)(58,71)(59,70)(60,66)(61,68)(62,67)(78,79)(81,91)(82,90)(83,92)(84,88)
(85,87)(86,89);
s3 := Sym(94)!( 3,51)( 4,52)( 5,53)( 6,48)( 7,49)( 8,50)( 9,60)(10,61)(11,62)
(12,57)(13,58)(14,59)(15,54)(16,55)(17,56)(18,66)(19,67)(20,68)(21,63)(22,64)
(23,65)(24,75)(25,76)(26,77)(27,72)(28,73)(29,74)(30,69)(31,70)(32,71)(33,81)
(34,82)(35,83)(36,78)(37,79)(38,80)(39,90)(40,91)(41,92)(42,87)(43,88)(44,89)
(45,84)(46,85)(47,86);
s4 := Sym(94)!(93,94);
poly := sub<Sym(94)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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 >;
to this polytope