Polytope of Type {35,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {35,2,2}*280
if this polytope has a name.
Group : SmallGroup(280,39)
Rank : 4
Schlafli Type : {35,2,2}
Number of vertices, edges, etc : 35, 35, 2, 2
Order of s₀s₁s₂s₃ : 70
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {35,2,2,2} of size 560
   {35,2,2,3} of size 840
   {35,2,2,4} of size 1120
   {35,2,2,5} of size 1400
   {35,2,2,6} of size 1680
   {35,2,2,7} of size 1960
Vertex Figure Of :
   {2,35,2,2} of size 560
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {7,2,2}*56
   7-fold quotients : {5,2,2}*40
Covers (Minimal Covers in Boldface) :
   2-fold covers : {35,2,4}*560, {70,2,2}*560
   3-fold covers : {35,2,6}*840, {105,2,2}*840
   4-fold covers : {35,2,8}*1120, {140,2,2}*1120, {70,2,4}*1120, {70,4,2}*1120
   5-fold covers : {175,2,2}*1400, {35,2,10}*1400, {35,10,2}*1400
   6-fold covers : {35,2,12}*1680, {105,2,4}*1680, {70,2,6}*1680, {70,6,2}*1680, {210,2,2}*1680
   7-fold covers : {245,2,2}*1960, {35,2,14}*1960, {35,14,2}*1960
Permutation Representation (GAP) :

s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)
(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)
(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34);;
s2 := (36,37);;
s3 := (38,39);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*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*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(39)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)
(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35);
s1 := Sym(39)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)
(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34);
s2 := Sym(39)!(36,37);
s3 := Sym(39)!(38,39);
poly := sub<Sym(39)|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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*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*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 >;

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