Polytope of Type {35,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {35,4}*1120
if this polytope has a name.
Group : SmallGroup(1120,1081)
Rank : 3
Schlafli Type : {35,4}
Number of vertices, edges, etc : 140, 280, 16
Order of s₀s₁s₂ : 35
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   7-fold quotients : {5,4}*160
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  3,  4)(  5,  6)(  9, 16)( 10, 15)( 11, 13)( 12, 14)( 17, 97)( 18, 98)
( 19,100)( 20, 99)( 21,102)( 22,101)( 23,103)( 24,104)( 25,112)( 26,111)
( 27,109)( 28,110)( 29,107)( 30,108)( 31,106)( 32,105)( 33, 81)( 34, 82)
( 35, 84)( 36, 83)( 37, 86)( 38, 85)( 39, 87)( 40, 88)( 41, 96)( 42, 95)
( 43, 93)( 44, 94)( 45, 91)( 46, 92)( 47, 90)( 48, 89)( 49, 65)( 50, 66)
( 51, 68)( 52, 67)( 53, 70)( 54, 69)( 55, 71)( 56, 72)( 57, 80)( 58, 79)
( 59, 77)( 60, 78)( 61, 75)( 62, 76)( 63, 74)( 64, 73);;
s1 := (  1, 17)(  2, 26)(  3, 27)(  4, 20)(  5, 32)(  6, 23)(  7, 22)(  8, 29)
(  9, 25)( 10, 18)( 11, 19)( 12, 28)( 13, 24)( 14, 31)( 15, 30)( 16, 21)
( 33, 97)( 34,106)( 35,107)( 36,100)( 37,112)( 38,103)( 39,102)( 40,109)
( 41,105)( 42, 98)( 43, 99)( 44,108)( 45,104)( 46,111)( 47,110)( 48,101)
( 49, 81)( 50, 90)( 51, 91)( 52, 84)( 53, 96)( 54, 87)( 55, 86)( 56, 93)
( 57, 89)( 58, 82)( 59, 83)( 60, 92)( 61, 88)( 62, 95)( 63, 94)( 64, 85)
( 66, 74)( 67, 75)( 69, 80)( 70, 71)( 72, 77)( 78, 79);;
s2 := (  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)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)
( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)
( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)
( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)
( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*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*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(112)!(  3,  4)(  5,  6)(  9, 16)( 10, 15)( 11, 13)( 12, 14)( 17, 97)
( 18, 98)( 19,100)( 20, 99)( 21,102)( 22,101)( 23,103)( 24,104)( 25,112)
( 26,111)( 27,109)( 28,110)( 29,107)( 30,108)( 31,106)( 32,105)( 33, 81)
( 34, 82)( 35, 84)( 36, 83)( 37, 86)( 38, 85)( 39, 87)( 40, 88)( 41, 96)
( 42, 95)( 43, 93)( 44, 94)( 45, 91)( 46, 92)( 47, 90)( 48, 89)( 49, 65)
( 50, 66)( 51, 68)( 52, 67)( 53, 70)( 54, 69)( 55, 71)( 56, 72)( 57, 80)
( 58, 79)( 59, 77)( 60, 78)( 61, 75)( 62, 76)( 63, 74)( 64, 73);
s1 := Sym(112)!(  1, 17)(  2, 26)(  3, 27)(  4, 20)(  5, 32)(  6, 23)(  7, 22)
(  8, 29)(  9, 25)( 10, 18)( 11, 19)( 12, 28)( 13, 24)( 14, 31)( 15, 30)
( 16, 21)( 33, 97)( 34,106)( 35,107)( 36,100)( 37,112)( 38,103)( 39,102)
( 40,109)( 41,105)( 42, 98)( 43, 99)( 44,108)( 45,104)( 46,111)( 47,110)
( 48,101)( 49, 81)( 50, 90)( 51, 91)( 52, 84)( 53, 96)( 54, 87)( 55, 86)
( 56, 93)( 57, 89)( 58, 82)( 59, 83)( 60, 92)( 61, 88)( 62, 95)( 63, 94)
( 64, 85)( 66, 74)( 67, 75)( 69, 80)( 70, 71)( 72, 77)( 78, 79);
s2 := Sym(112)!(  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)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)
( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)
( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)
( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)
( 95, 96)( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)
(111,112);
poly := sub<Sym(112)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*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*s0*s1 >;

References : None.
to this polytope