Polytope of Type {2,14,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,14,20}*1120
if this polytope has a name.
Group : SmallGroup(1120,988)
Rank : 4
Schlafli Type : {2,14,20}
Number of vertices, edges, etc : 2, 14, 140, 20
Order of s₀s₁s₂s₃ : 140
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,14,10}*560
   5-fold quotients : {2,14,4}*224
   7-fold quotients : {2,2,20}*160
   10-fold quotients : {2,14,2}*112
   14-fold quotients : {2,2,10}*80
   20-fold quotients : {2,7,2}*56
   28-fold quotients : {2,2,5}*40
   35-fold quotients : {2,2,4}*32
   70-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4,  9)(  5,  8)(  6,  7)( 11, 16)( 12, 15)( 13, 14)( 18, 23)( 19, 22)
( 20, 21)( 25, 30)( 26, 29)( 27, 28)( 32, 37)( 33, 36)( 34, 35)( 39, 44)
( 40, 43)( 41, 42)( 46, 51)( 47, 50)( 48, 49)( 53, 58)( 54, 57)( 55, 56)
( 60, 65)( 61, 64)( 62, 63)( 67, 72)( 68, 71)( 69, 70)( 74, 79)( 75, 78)
( 76, 77)( 81, 86)( 82, 85)( 83, 84)( 88, 93)( 89, 92)( 90, 91)( 95,100)
( 96, 99)( 97, 98)(102,107)(103,106)(104,105)(109,114)(110,113)(111,112)
(116,121)(117,120)(118,119)(123,128)(124,127)(125,126)(130,135)(131,134)
(132,133)(137,142)(138,141)(139,140);;
s2 := (  3,  4)(  5,  9)(  6,  8)( 10, 32)( 11, 31)( 12, 37)( 13, 36)( 14, 35)
( 15, 34)( 16, 33)( 17, 25)( 18, 24)( 19, 30)( 20, 29)( 21, 28)( 22, 27)
( 23, 26)( 38, 39)( 40, 44)( 41, 43)( 45, 67)( 46, 66)( 47, 72)( 48, 71)
( 49, 70)( 50, 69)( 51, 68)( 52, 60)( 53, 59)( 54, 65)( 55, 64)( 56, 63)
( 57, 62)( 58, 61)( 73,109)( 74,108)( 75,114)( 76,113)( 77,112)( 78,111)
( 79,110)( 80,137)( 81,136)( 82,142)( 83,141)( 84,140)( 85,139)( 86,138)
( 87,130)( 88,129)( 89,135)( 90,134)( 91,133)( 92,132)( 93,131)( 94,123)
( 95,122)( 96,128)( 97,127)( 98,126)( 99,125)(100,124)(101,116)(102,115)
(103,121)(104,120)(105,119)(106,118)(107,117);;
s3 := (  3, 80)(  4, 81)(  5, 82)(  6, 83)(  7, 84)(  8, 85)(  9, 86)( 10, 73)
( 11, 74)( 12, 75)( 13, 76)( 14, 77)( 15, 78)( 16, 79)( 17,101)( 18,102)
( 19,103)( 20,104)( 21,105)( 22,106)( 23,107)( 24, 94)( 25, 95)( 26, 96)
( 27, 97)( 28, 98)( 29, 99)( 30,100)( 31, 87)( 32, 88)( 33, 89)( 34, 90)
( 35, 91)( 36, 92)( 37, 93)( 38,115)( 39,116)( 40,117)( 41,118)( 42,119)
( 43,120)( 44,121)( 45,108)( 46,109)( 47,110)( 48,111)( 49,112)( 50,113)
( 51,114)( 52,136)( 53,137)( 54,138)( 55,139)( 56,140)( 57,141)( 58,142)
( 59,129)( 60,130)( 61,131)( 62,132)( 63,133)( 64,134)( 65,135)( 66,122)
( 67,123)( 68,124)( 69,125)( 70,126)( 71,127)( 72,128);;
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, 
s1*s2*s3*s2*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(142)!(1,2);
s1 := Sym(142)!(  4,  9)(  5,  8)(  6,  7)( 11, 16)( 12, 15)( 13, 14)( 18, 23)
( 19, 22)( 20, 21)( 25, 30)( 26, 29)( 27, 28)( 32, 37)( 33, 36)( 34, 35)
( 39, 44)( 40, 43)( 41, 42)( 46, 51)( 47, 50)( 48, 49)( 53, 58)( 54, 57)
( 55, 56)( 60, 65)( 61, 64)( 62, 63)( 67, 72)( 68, 71)( 69, 70)( 74, 79)
( 75, 78)( 76, 77)( 81, 86)( 82, 85)( 83, 84)( 88, 93)( 89, 92)( 90, 91)
( 95,100)( 96, 99)( 97, 98)(102,107)(103,106)(104,105)(109,114)(110,113)
(111,112)(116,121)(117,120)(118,119)(123,128)(124,127)(125,126)(130,135)
(131,134)(132,133)(137,142)(138,141)(139,140);
s2 := Sym(142)!(  3,  4)(  5,  9)(  6,  8)( 10, 32)( 11, 31)( 12, 37)( 13, 36)
( 14, 35)( 15, 34)( 16, 33)( 17, 25)( 18, 24)( 19, 30)( 20, 29)( 21, 28)
( 22, 27)( 23, 26)( 38, 39)( 40, 44)( 41, 43)( 45, 67)( 46, 66)( 47, 72)
( 48, 71)( 49, 70)( 50, 69)( 51, 68)( 52, 60)( 53, 59)( 54, 65)( 55, 64)
( 56, 63)( 57, 62)( 58, 61)( 73,109)( 74,108)( 75,114)( 76,113)( 77,112)
( 78,111)( 79,110)( 80,137)( 81,136)( 82,142)( 83,141)( 84,140)( 85,139)
( 86,138)( 87,130)( 88,129)( 89,135)( 90,134)( 91,133)( 92,132)( 93,131)
( 94,123)( 95,122)( 96,128)( 97,127)( 98,126)( 99,125)(100,124)(101,116)
(102,115)(103,121)(104,120)(105,119)(106,118)(107,117);
s3 := Sym(142)!(  3, 80)(  4, 81)(  5, 82)(  6, 83)(  7, 84)(  8, 85)(  9, 86)
( 10, 73)( 11, 74)( 12, 75)( 13, 76)( 14, 77)( 15, 78)( 16, 79)( 17,101)
( 18,102)( 19,103)( 20,104)( 21,105)( 22,106)( 23,107)( 24, 94)( 25, 95)
( 26, 96)( 27, 97)( 28, 98)( 29, 99)( 30,100)( 31, 87)( 32, 88)( 33, 89)
( 34, 90)( 35, 91)( 36, 92)( 37, 93)( 38,115)( 39,116)( 40,117)( 41,118)
( 42,119)( 43,120)( 44,121)( 45,108)( 46,109)( 47,110)( 48,111)( 49,112)
( 50,113)( 51,114)( 52,136)( 53,137)( 54,138)( 55,139)( 56,140)( 57,141)
( 58,142)( 59,129)( 60,130)( 61,131)( 62,132)( 63,133)( 64,134)( 65,135)
( 66,122)( 67,123)( 68,124)( 69,125)( 70,126)( 71,127)( 72,128);
poly := sub<Sym(142)|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, s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope