Polytope of Type {2,20,14}

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

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