Polytope of Type {2,2,20,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,20,8}*1280a
if this polytope has a name.
Group : SmallGroup(1280,1035863)
Rank : 5
Schlafli Type : {2,2,20,8}
Number of vertices, edges, etc : 2, 2, 20, 80, 8
Order of s0s1s2s3s4 : 40
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) :
2-fold quotients : {2,2,20,4}*640, {2,2,10,8}*640
4-fold quotients : {2,2,20,2}*320, {2,2,10,4}*320
5-fold quotients : {2,2,4,8}*256a
8-fold quotients : {2,2,10,2}*160
10-fold quotients : {2,2,4,4}*128, {2,2,2,8}*128
16-fold quotients : {2,2,5,2}*80
20-fold quotients : {2,2,2,4}*64, {2,2,4,2}*64
40-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 9)( 7, 8)(11,14)(12,13)(16,19)(17,18)(21,24)(22,23)(26,29)(27,28)
(31,34)(32,33)(36,39)(37,38)(41,44)(42,43)(45,65)(46,69)(47,68)(48,67)(49,66)
(50,70)(51,74)(52,73)(53,72)(54,71)(55,75)(56,79)(57,78)(58,77)(59,76)(60,80)
(61,84)(62,83)(63,82)(64,81);;
s3 := ( 5,46)( 6,45)( 7,49)( 8,48)( 9,47)(10,51)(11,50)(12,54)(13,53)(14,52)
(15,61)(16,60)(17,64)(18,63)(19,62)(20,56)(21,55)(22,59)(23,58)(24,57)(25,66)
(26,65)(27,69)(28,68)(29,67)(30,71)(31,70)(32,74)(33,73)(34,72)(35,81)(36,80)
(37,84)(38,83)(39,82)(40,76)(41,75)(42,79)(43,78)(44,77);;
s4 := (15,20)(16,21)(17,22)(18,23)(19,24)(35,40)(36,41)(37,42)(38,43)(39,44)
(45,55)(46,56)(47,57)(48,58)(49,59)(50,60)(51,61)(52,62)(53,63)(54,64)(65,75)
(66,76)(67,77)(68,78)(69,79)(70,80)(71,81)(72,82)(73,83)(74,84);;
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, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(84)!(1,2);
s1 := Sym(84)!(3,4);
s2 := Sym(84)!( 6, 9)( 7, 8)(11,14)(12,13)(16,19)(17,18)(21,24)(22,23)(26,29)
(27,28)(31,34)(32,33)(36,39)(37,38)(41,44)(42,43)(45,65)(46,69)(47,68)(48,67)
(49,66)(50,70)(51,74)(52,73)(53,72)(54,71)(55,75)(56,79)(57,78)(58,77)(59,76)
(60,80)(61,84)(62,83)(63,82)(64,81);
s3 := Sym(84)!( 5,46)( 6,45)( 7,49)( 8,48)( 9,47)(10,51)(11,50)(12,54)(13,53)
(14,52)(15,61)(16,60)(17,64)(18,63)(19,62)(20,56)(21,55)(22,59)(23,58)(24,57)
(25,66)(26,65)(27,69)(28,68)(29,67)(30,71)(31,70)(32,74)(33,73)(34,72)(35,81)
(36,80)(37,84)(38,83)(39,82)(40,76)(41,75)(42,79)(43,78)(44,77);
s4 := Sym(84)!(15,20)(16,21)(17,22)(18,23)(19,24)(35,40)(36,41)(37,42)(38,43)
(39,44)(45,55)(46,56)(47,57)(48,58)(49,59)(50,60)(51,61)(52,62)(53,63)(54,64)
(65,75)(66,76)(67,77)(68,78)(69,79)(70,80)(71,81)(72,82)(73,83)(74,84);
poly := sub<Sym(84)|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,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope