Polytope of Type {2,2,10,4,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,10,4,4}*1280
if this polytope has a name.
Group : SmallGroup(1280,1076197)
Rank : 6
Schlafli Type : {2,2,10,4,4}
Number of vertices, edges, etc : 2, 2, 10, 20, 8, 4
Order of s0s1s2s3s4s5 : 20
Order of s0s1s2s3s4s5s4s3s2s1 : 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 : {2,2,10,2,4}*640, {2,2,10,4,2}*640
4-fold quotients : {2,2,5,2,4}*320, {2,2,10,2,2}*320
5-fold quotients : {2,2,2,4,4}*256
8-fold quotients : {2,2,5,2,2}*160
10-fold quotients : {2,2,2,2,4}*128, {2,2,2,4,2}*128
20-fold quotients : {2,2,2,2,2}*64
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)(46,49)(47,48)(51,54)(52,53)(56,59)
(57,58)(61,64)(62,63)(66,69)(67,68)(71,74)(72,73)(76,79)(77,78)(81,84)
(82,83);;
s3 := ( 5, 6)( 7, 9)(10,11)(12,14)(15,16)(17,19)(20,21)(22,24)(25,31)(26,30)
(27,34)(28,33)(29,32)(35,41)(36,40)(37,44)(38,43)(39,42)(45,46)(47,49)(50,51)
(52,54)(55,56)(57,59)(60,61)(62,64)(65,71)(66,70)(67,74)(68,73)(69,72)(75,81)
(76,80)(77,84)(78,83)(79,82);;
s4 := ( 5,25)( 6,26)( 7,27)( 8,28)( 9,29)(10,30)(11,31)(12,32)(13,33)(14,34)
(15,35)(16,36)(17,37)(18,38)(19,39)(20,40)(21,41)(22,42)(23,43)(24,44)(45,65)
(46,66)(47,67)(48,68)(49,69)(50,70)(51,71)(52,72)(53,73)(54,74)(55,75)(56,76)
(57,77)(58,78)(59,79)(60,80)(61,81)(62,82)(63,83)(64,84);;
s5 := ( 5,45)( 6,46)( 7,47)( 8,48)( 9,49)(10,50)(11,51)(12,52)(13,53)(14,54)
(15,55)(16,56)(17,57)(18,58)(19,59)(20,60)(21,61)(22,62)(23,63)(24,64)(25,75)
(26,76)(27,77)(28,78)(29,79)(30,80)(31,81)(32,82)(33,83)(34,84)(35,65)(36,66)
(37,67)(38,68)(39,69)(40,70)(41,71)(42,72)(43,73)(44,74);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
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, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4,
s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5,
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)(46,49)(47,48)(51,54)(52,53)
(56,59)(57,58)(61,64)(62,63)(66,69)(67,68)(71,74)(72,73)(76,79)(77,78)(81,84)
(82,83);
s3 := Sym(84)!( 5, 6)( 7, 9)(10,11)(12,14)(15,16)(17,19)(20,21)(22,24)(25,31)
(26,30)(27,34)(28,33)(29,32)(35,41)(36,40)(37,44)(38,43)(39,42)(45,46)(47,49)
(50,51)(52,54)(55,56)(57,59)(60,61)(62,64)(65,71)(66,70)(67,74)(68,73)(69,72)
(75,81)(76,80)(77,84)(78,83)(79,82);
s4 := Sym(84)!( 5,25)( 6,26)( 7,27)( 8,28)( 9,29)(10,30)(11,31)(12,32)(13,33)
(14,34)(15,35)(16,36)(17,37)(18,38)(19,39)(20,40)(21,41)(22,42)(23,43)(24,44)
(45,65)(46,66)(47,67)(48,68)(49,69)(50,70)(51,71)(52,72)(53,73)(54,74)(55,75)
(56,76)(57,77)(58,78)(59,79)(60,80)(61,81)(62,82)(63,83)(64,84);
s5 := Sym(84)!( 5,45)( 6,46)( 7,47)( 8,48)( 9,49)(10,50)(11,51)(12,52)(13,53)
(14,54)(15,55)(16,56)(17,57)(18,58)(19,59)(20,60)(21,61)(22,62)(23,63)(24,64)
(25,75)(26,76)(27,77)(28,78)(29,79)(30,80)(31,81)(32,82)(33,83)(34,84)(35,65)
(36,66)(37,67)(38,68)(39,69)(40,70)(41,71)(42,72)(43,73)(44,74);
poly := sub<Sym(84)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, 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,
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, s3*s4*s5*s4*s3*s4*s5*s4,
s4*s5*s4*s5*s4*s5*s4*s5, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope