Polytope of Type {140}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {140}*280
Also Known As : 140-gon, {140}. if this polytope has another name.
Group : SmallGroup(280,26)
Rank : 2
Schlafli Type : {140}
Number of vertices, edges, etc : 140, 140
Order of s0s1 : 140
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{140,2} of size 560
{140,4} of size 1120
{140,6} of size 1680
{140,6} of size 1680
Vertex Figure Of :
{2,140} of size 560
{4,140} of size 1120
{6,140} of size 1680
{6,140} of size 1680
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {70}*140
4-fold quotients : {35}*70
5-fold quotients : {28}*56
7-fold quotients : {20}*40
10-fold quotients : {14}*28
14-fold quotients : {10}*20
20-fold quotients : {7}*14
28-fold quotients : {5}*10
35-fold quotients : {4}*8
70-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
2-fold covers : {280}*560
3-fold covers : {420}*840
4-fold covers : {560}*1120
5-fold covers : {700}*1400
6-fold covers : {840}*1680
7-fold covers : {980}*1960
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);;
poly := Group([s0,s1]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1");;
s0 := F.1;; s1 := F.2;;
rels := [ s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(140)!( 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(140)!( 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);
poly := sub<Sym(140)|s0,s1>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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.
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