Polytope of Type {140,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {140,2}*560
if this polytope has a name.
Group : SmallGroup(560,158)
Rank : 3
Schlafli Type : {140,2}
Number of vertices, edges, etc : 140, 140, 2
Order of s0s1s2 : 140
Order of s0s1s2s1 : 2
Special Properties :
Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{140,2,2} of size 1120
{140,2,3} of size 1680
Vertex Figure Of :
{2,140,2} of size 1120
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {70,2}*280
4-fold quotients : {35,2}*140
5-fold quotients : {28,2}*112
7-fold quotients : {20,2}*80
10-fold quotients : {14,2}*56
14-fold quotients : {10,2}*40
20-fold quotients : {7,2}*28
28-fold quotients : {5,2}*20
35-fold quotients : {4,2}*16
70-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {140,4}*1120, {280,2}*1120
3-fold covers : {140,6}*1680a, {420,2}*1680
Permutation Representation (GAP) :
s0 := ( 2, 7)( 3, 6)( 4, 5)( 8, 29)( 9, 35)( 10, 34)( 11, 33)( 12, 32)
( 13, 31)( 14, 30)( 15, 22)( 16, 28)( 17, 27)( 18, 26)( 19, 25)( 20, 24)
( 21, 23)( 37, 42)( 38, 41)( 39, 40)( 43, 64)( 44, 70)( 45, 69)( 46, 68)
( 47, 67)( 48, 66)( 49, 65)( 50, 57)( 51, 63)( 52, 62)( 53, 61)( 54, 60)
( 55, 59)( 56, 58)( 71,106)( 72,112)( 73,111)( 74,110)( 75,109)( 76,108)
( 77,107)( 78,134)( 79,140)( 80,139)( 81,138)( 82,137)( 83,136)( 84,135)
( 85,127)( 86,133)( 87,132)( 88,131)( 89,130)( 90,129)( 91,128)( 92,120)
( 93,126)( 94,125)( 95,124)( 96,123)( 97,122)( 98,121)( 99,113)(100,119)
(101,118)(102,117)(103,116)(104,115)(105,114);;
s1 := ( 1, 79)( 2, 78)( 3, 84)( 4, 83)( 5, 82)( 6, 81)( 7, 80)( 8, 72)
( 9, 71)( 10, 77)( 11, 76)( 12, 75)( 13, 74)( 14, 73)( 15,100)( 16, 99)
( 17,105)( 18,104)( 19,103)( 20,102)( 21,101)( 22, 93)( 23, 92)( 24, 98)
( 25, 97)( 26, 96)( 27, 95)( 28, 94)( 29, 86)( 30, 85)( 31, 91)( 32, 90)
( 33, 89)( 34, 88)( 35, 87)( 36,114)( 37,113)( 38,119)( 39,118)( 40,117)
( 41,116)( 42,115)( 43,107)( 44,106)( 45,112)( 46,111)( 47,110)( 48,109)
( 49,108)( 50,135)( 51,134)( 52,140)( 53,139)( 54,138)( 55,137)( 56,136)
( 57,128)( 58,127)( 59,133)( 60,132)( 61,131)( 62,130)( 63,129)( 64,121)
( 65,120)( 66,126)( 67,125)( 68,124)( 69,123)( 70,122);;
s2 := (141,142);;
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,
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*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*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*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(142)!( 2, 7)( 3, 6)( 4, 5)( 8, 29)( 9, 35)( 10, 34)( 11, 33)
( 12, 32)( 13, 31)( 14, 30)( 15, 22)( 16, 28)( 17, 27)( 18, 26)( 19, 25)
( 20, 24)( 21, 23)( 37, 42)( 38, 41)( 39, 40)( 43, 64)( 44, 70)( 45, 69)
( 46, 68)( 47, 67)( 48, 66)( 49, 65)( 50, 57)( 51, 63)( 52, 62)( 53, 61)
( 54, 60)( 55, 59)( 56, 58)( 71,106)( 72,112)( 73,111)( 74,110)( 75,109)
( 76,108)( 77,107)( 78,134)( 79,140)( 80,139)( 81,138)( 82,137)( 83,136)
( 84,135)( 85,127)( 86,133)( 87,132)( 88,131)( 89,130)( 90,129)( 91,128)
( 92,120)( 93,126)( 94,125)( 95,124)( 96,123)( 97,122)( 98,121)( 99,113)
(100,119)(101,118)(102,117)(103,116)(104,115)(105,114);
s1 := Sym(142)!( 1, 79)( 2, 78)( 3, 84)( 4, 83)( 5, 82)( 6, 81)( 7, 80)
( 8, 72)( 9, 71)( 10, 77)( 11, 76)( 12, 75)( 13, 74)( 14, 73)( 15,100)
( 16, 99)( 17,105)( 18,104)( 19,103)( 20,102)( 21,101)( 22, 93)( 23, 92)
( 24, 98)( 25, 97)( 26, 96)( 27, 95)( 28, 94)( 29, 86)( 30, 85)( 31, 91)
( 32, 90)( 33, 89)( 34, 88)( 35, 87)( 36,114)( 37,113)( 38,119)( 39,118)
( 40,117)( 41,116)( 42,115)( 43,107)( 44,106)( 45,112)( 46,111)( 47,110)
( 48,109)( 49,108)( 50,135)( 51,134)( 52,140)( 53,139)( 54,138)( 55,137)
( 56,136)( 57,128)( 58,127)( 59,133)( 60,132)( 61,131)( 62,130)( 63,129)
( 64,121)( 65,120)( 66,126)( 67,125)( 68,124)( 69,123)( 70,122);
s2 := Sym(142)!(141,142);
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*s2*s0*s2, s1*s2*s1*s2, 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*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*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*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 >;
to this polytope