Polytope of Type {2,8,20,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,20,2}*1280a
if this polytope has a name.
Group : SmallGroup(1280,1035863)
Rank : 5
Schlafli Type : {2,8,20,2}
Number of vertices, edges, etc : 2, 8, 80, 20, 2
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 : {2,4,20,2}*640, {2,8,10,2}*640
4-fold quotients : {2,2,20,2}*320, {2,4,10,2}*320
5-fold quotients : {2,8,4,2}*256a
8-fold quotients : {2,2,10,2}*160
10-fold quotients : {2,4,4,2}*128, {2,8,2,2}*128
16-fold quotients : {2,2,5,2}*80
20-fold quotients : {2,2,4,2}*64, {2,4,2,2}*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 := (13,18)(14,19)(15,20)(16,21)(17,22)(33,38)(34,39)(35,40)(36,41)(37,42)
(43,53)(44,54)(45,55)(46,56)(47,57)(48,58)(49,59)(50,60)(51,61)(52,62)(63,73)
(64,74)(65,75)(66,76)(67,77)(68,78)(69,79)(70,80)(71,81)(72,82);;
s2 := ( 3,43)( 4,47)( 5,46)( 6,45)( 7,44)( 8,48)( 9,52)(10,51)(11,50)(12,49)
(13,58)(14,62)(15,61)(16,60)(17,59)(18,53)(19,57)(20,56)(21,55)(22,54)(23,63)
(24,67)(25,66)(26,65)(27,64)(28,68)(29,72)(30,71)(31,70)(32,69)(33,78)(34,82)
(35,81)(36,80)(37,79)(38,73)(39,77)(40,76)(41,75)(42,74);;
s3 := ( 3, 4)( 5, 7)( 8, 9)(10,12)(13,14)(15,17)(18,19)(20,22)(23,24)(25,27)
(28,29)(30,32)(33,34)(35,37)(38,39)(40,42)(43,64)(44,63)(45,67)(46,66)(47,65)
(48,69)(49,68)(50,72)(51,71)(52,70)(53,74)(54,73)(55,77)(56,76)(57,75)(58,79)
(59,78)(60,82)(61,81)(62,80);;
s4 := (83,84);;
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, 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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
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)!(13,18)(14,19)(15,20)(16,21)(17,22)(33,38)(34,39)(35,40)(36,41)
(37,42)(43,53)(44,54)(45,55)(46,56)(47,57)(48,58)(49,59)(50,60)(51,61)(52,62)
(63,73)(64,74)(65,75)(66,76)(67,77)(68,78)(69,79)(70,80)(71,81)(72,82);
s2 := Sym(84)!( 3,43)( 4,47)( 5,46)( 6,45)( 7,44)( 8,48)( 9,52)(10,51)(11,50)
(12,49)(13,58)(14,62)(15,61)(16,60)(17,59)(18,53)(19,57)(20,56)(21,55)(22,54)
(23,63)(24,67)(25,66)(26,65)(27,64)(28,68)(29,72)(30,71)(31,70)(32,69)(33,78)
(34,82)(35,81)(36,80)(37,79)(38,73)(39,77)(40,76)(41,75)(42,74);
s3 := Sym(84)!( 3, 4)( 5, 7)( 8, 9)(10,12)(13,14)(15,17)(18,19)(20,22)(23,24)
(25,27)(28,29)(30,32)(33,34)(35,37)(38,39)(40,42)(43,64)(44,63)(45,67)(46,66)
(47,65)(48,69)(49,68)(50,72)(51,71)(52,70)(53,74)(54,73)(55,77)(56,76)(57,75)
(58,79)(59,78)(60,82)(61,81)(62,80);
s4 := Sym(84)!(83,84);
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,
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
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