Polytope of Type {2,35,2}

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

s0 := (1,2);;
s1 := ( 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)(36,37);;
s2 := ( 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)(35,36);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*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*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(39)!(1,2);
s1 := Sym(39)!( 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)(36,37);
s2 := Sym(39)!( 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)(35,36);
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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*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*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