Polytope of Type {2,140}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,140}*560
if this polytope has a name.
Group : SmallGroup(560,158)
Rank : 3
Schlafli Type : {2,140}
Number of vertices, edges, etc : 2, 140, 140
Order of s₀s₁s₂ : 140
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,140,2} of size 1120
Vertex Figure Of :
   {2,2,140} of size 1120
   {3,2,140} of size 1680
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,70}*280
   4-fold quotients : {2,35}*140
   5-fold quotients : {2,28}*112
   7-fold quotients : {2,20}*80
   10-fold quotients : {2,14}*56
   14-fold quotients : {2,10}*40
   20-fold quotients : {2,7}*28
   28-fold quotients : {2,5}*20
   35-fold quotients : {2,4}*16
   70-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,140}*1120, {2,280}*1120
   3-fold covers : {6,140}*1680a, {2,420}*1680
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4,  9)(  5,  8)(  6,  7)( 10, 31)( 11, 37)( 12, 36)( 13, 35)( 14, 34)
( 15, 33)( 16, 32)( 17, 24)( 18, 30)( 19, 29)( 20, 28)( 21, 27)( 22, 26)
( 23, 25)( 39, 44)( 40, 43)( 41, 42)( 45, 66)( 46, 72)( 47, 71)( 48, 70)
( 49, 69)( 50, 68)( 51, 67)( 52, 59)( 53, 65)( 54, 64)( 55, 63)( 56, 62)
( 57, 61)( 58, 60)( 73,108)( 74,114)( 75,113)( 76,112)( 77,111)( 78,110)
( 79,109)( 80,136)( 81,142)( 82,141)( 83,140)( 84,139)( 85,138)( 86,137)
( 87,129)( 88,135)( 89,134)( 90,133)( 91,132)( 92,131)( 93,130)( 94,122)
( 95,128)( 96,127)( 97,126)( 98,125)( 99,124)(100,123)(101,115)(102,121)
(103,120)(104,119)(105,118)(106,117)(107,116);;
s2 := (  3, 81)(  4, 80)(  5, 86)(  6, 85)(  7, 84)(  8, 83)(  9, 82)( 10, 74)
( 11, 73)( 12, 79)( 13, 78)( 14, 77)( 15, 76)( 16, 75)( 17,102)( 18,101)
( 19,107)( 20,106)( 21,105)( 22,104)( 23,103)( 24, 95)( 25, 94)( 26,100)
( 27, 99)( 28, 98)( 29, 97)( 30, 96)( 31, 88)( 32, 87)( 33, 93)( 34, 92)
( 35, 91)( 36, 90)( 37, 89)( 38,116)( 39,115)( 40,121)( 41,120)( 42,119)
( 43,118)( 44,117)( 45,109)( 46,108)( 47,114)( 48,113)( 49,112)( 50,111)
( 51,110)( 52,137)( 53,136)( 54,142)( 55,141)( 56,140)( 57,139)( 58,138)
( 59,130)( 60,129)( 61,135)( 62,134)( 63,133)( 64,132)( 65,131)( 66,123)
( 67,122)( 68,128)( 69,127)( 70,126)( 71,125)( 72,124);;
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*s1*s0*s1, s0*s2*s0*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*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*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*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*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(142)!(1,2);
s1 := Sym(142)!(  4,  9)(  5,  8)(  6,  7)( 10, 31)( 11, 37)( 12, 36)( 13, 35)
( 14, 34)( 15, 33)( 16, 32)( 17, 24)( 18, 30)( 19, 29)( 20, 28)( 21, 27)
( 22, 26)( 23, 25)( 39, 44)( 40, 43)( 41, 42)( 45, 66)( 46, 72)( 47, 71)
( 48, 70)( 49, 69)( 50, 68)( 51, 67)( 52, 59)( 53, 65)( 54, 64)( 55, 63)
( 56, 62)( 57, 61)( 58, 60)( 73,108)( 74,114)( 75,113)( 76,112)( 77,111)
( 78,110)( 79,109)( 80,136)( 81,142)( 82,141)( 83,140)( 84,139)( 85,138)
( 86,137)( 87,129)( 88,135)( 89,134)( 90,133)( 91,132)( 92,131)( 93,130)
( 94,122)( 95,128)( 96,127)( 97,126)( 98,125)( 99,124)(100,123)(101,115)
(102,121)(103,120)(104,119)(105,118)(106,117)(107,116);
s2 := Sym(142)!(  3, 81)(  4, 80)(  5, 86)(  6, 85)(  7, 84)(  8, 83)(  9, 82)
( 10, 74)( 11, 73)( 12, 79)( 13, 78)( 14, 77)( 15, 76)( 16, 75)( 17,102)
( 18,101)( 19,107)( 20,106)( 21,105)( 22,104)( 23,103)( 24, 95)( 25, 94)
( 26,100)( 27, 99)( 28, 98)( 29, 97)( 30, 96)( 31, 88)( 32, 87)( 33, 93)
( 34, 92)( 35, 91)( 36, 90)( 37, 89)( 38,116)( 39,115)( 40,121)( 41,120)
( 42,119)( 43,118)( 44,117)( 45,109)( 46,108)( 47,114)( 48,113)( 49,112)
( 50,111)( 51,110)( 52,137)( 53,136)( 54,142)( 55,141)( 56,140)( 57,139)
( 58,138)( 59,130)( 60,129)( 61,135)( 62,134)( 63,133)( 64,132)( 65,131)
( 66,123)( 67,122)( 68,128)( 69,127)( 70,126)( 71,125)( 72,124);
poly := sub<Sym(142)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

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

to this polytope