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Polytope of Type {20,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,14}*560
Also Known As : {20,14|2}. if this polytope has another name.
Group : SmallGroup(560,120)
Rank : 3
Schlafli Type : {20,14}
Number of vertices, edges, etc : 20, 140, 14
Order of s0s1s2 : 140
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {20,14,2} of size 1120
Vertex Figure Of :
   {2,20,14} of size 1120
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,14}*280
   5-fold quotients : {4,14}*112
   7-fold quotients : {20,2}*80
   10-fold quotients : {2,14}*56
   14-fold quotients : {10,2}*40
   20-fold quotients : {2,7}*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 : {40,14}*1120, {20,28}*1120
   3-fold covers : {60,14}*1680, {20,42}*1680a
Permutation Representation (GAP) :
s0 := (  8, 29)(  9, 30)( 10, 31)( 11, 32)( 12, 33)( 13, 34)( 14, 35)( 15, 22)
( 16, 23)( 17, 24)( 18, 25)( 19, 26)( 20, 27)( 21, 28)( 43, 64)( 44, 65)
( 45, 66)( 46, 67)( 47, 68)( 48, 69)( 49, 70)( 50, 57)( 51, 58)( 52, 59)
( 53, 60)( 54, 61)( 55, 62)( 56, 63)( 71,106)( 72,107)( 73,108)( 74,109)
( 75,110)( 76,111)( 77,112)( 78,134)( 79,135)( 80,136)( 81,137)( 82,138)
( 83,139)( 84,140)( 85,127)( 86,128)( 87,129)( 88,130)( 89,131)( 90,132)
( 91,133)( 92,120)( 93,121)( 94,122)( 95,123)( 96,124)( 97,125)( 98,126)
( 99,113)(100,114)(101,115)(102,116)(103,117)(104,118)(105,119);;
s1 := (  1, 78)(  2, 84)(  3, 83)(  4, 82)(  5, 81)(  6, 80)(  7, 79)(  8, 71)
(  9, 77)( 10, 76)( 11, 75)( 12, 74)( 13, 73)( 14, 72)( 15, 99)( 16,105)
( 17,104)( 18,103)( 19,102)( 20,101)( 21,100)( 22, 92)( 23, 98)( 24, 97)
( 25, 96)( 26, 95)( 27, 94)( 28, 93)( 29, 85)( 30, 91)( 31, 90)( 32, 89)
( 33, 88)( 34, 87)( 35, 86)( 36,113)( 37,119)( 38,118)( 39,117)( 40,116)
( 41,115)( 42,114)( 43,106)( 44,112)( 45,111)( 46,110)( 47,109)( 48,108)
( 49,107)( 50,134)( 51,140)( 52,139)( 53,138)( 54,137)( 55,136)( 56,135)
( 57,127)( 58,133)( 59,132)( 60,131)( 61,130)( 62,129)( 63,128)( 64,120)
( 65,126)( 66,125)( 67,124)( 68,123)( 69,122)( 70,121);;
s2 := (  1,  2)(  3,  7)(  4,  6)(  8,  9)( 10, 14)( 11, 13)( 15, 16)( 17, 21)
( 18, 20)( 22, 23)( 24, 28)( 25, 27)( 29, 30)( 31, 35)( 32, 34)( 36, 37)
( 38, 42)( 39, 41)( 43, 44)( 45, 49)( 46, 48)( 50, 51)( 52, 56)( 53, 55)
( 57, 58)( 59, 63)( 60, 62)( 64, 65)( 66, 70)( 67, 69)( 71, 72)( 73, 77)
( 74, 76)( 78, 79)( 80, 84)( 81, 83)( 85, 86)( 87, 91)( 88, 90)( 92, 93)
( 94, 98)( 95, 97)( 99,100)(101,105)(102,104)(106,107)(108,112)(109,111)
(113,114)(115,119)(116,118)(120,121)(122,126)(123,125)(127,128)(129,133)
(130,132)(134,135)(136,140)(137,139);;
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, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(140)!(  8, 29)(  9, 30)( 10, 31)( 11, 32)( 12, 33)( 13, 34)( 14, 35)
( 15, 22)( 16, 23)( 17, 24)( 18, 25)( 19, 26)( 20, 27)( 21, 28)( 43, 64)
( 44, 65)( 45, 66)( 46, 67)( 47, 68)( 48, 69)( 49, 70)( 50, 57)( 51, 58)
( 52, 59)( 53, 60)( 54, 61)( 55, 62)( 56, 63)( 71,106)( 72,107)( 73,108)
( 74,109)( 75,110)( 76,111)( 77,112)( 78,134)( 79,135)( 80,136)( 81,137)
( 82,138)( 83,139)( 84,140)( 85,127)( 86,128)( 87,129)( 88,130)( 89,131)
( 90,132)( 91,133)( 92,120)( 93,121)( 94,122)( 95,123)( 96,124)( 97,125)
( 98,126)( 99,113)(100,114)(101,115)(102,116)(103,117)(104,118)(105,119);
s1 := Sym(140)!(  1, 78)(  2, 84)(  3, 83)(  4, 82)(  5, 81)(  6, 80)(  7, 79)
(  8, 71)(  9, 77)( 10, 76)( 11, 75)( 12, 74)( 13, 73)( 14, 72)( 15, 99)
( 16,105)( 17,104)( 18,103)( 19,102)( 20,101)( 21,100)( 22, 92)( 23, 98)
( 24, 97)( 25, 96)( 26, 95)( 27, 94)( 28, 93)( 29, 85)( 30, 91)( 31, 90)
( 32, 89)( 33, 88)( 34, 87)( 35, 86)( 36,113)( 37,119)( 38,118)( 39,117)
( 40,116)( 41,115)( 42,114)( 43,106)( 44,112)( 45,111)( 46,110)( 47,109)
( 48,108)( 49,107)( 50,134)( 51,140)( 52,139)( 53,138)( 54,137)( 55,136)
( 56,135)( 57,127)( 58,133)( 59,132)( 60,131)( 61,130)( 62,129)( 63,128)
( 64,120)( 65,126)( 66,125)( 67,124)( 68,123)( 69,122)( 70,121);
s2 := Sym(140)!(  1,  2)(  3,  7)(  4,  6)(  8,  9)( 10, 14)( 11, 13)( 15, 16)
( 17, 21)( 18, 20)( 22, 23)( 24, 28)( 25, 27)( 29, 30)( 31, 35)( 32, 34)
( 36, 37)( 38, 42)( 39, 41)( 43, 44)( 45, 49)( 46, 48)( 50, 51)( 52, 56)
( 53, 55)( 57, 58)( 59, 63)( 60, 62)( 64, 65)( 66, 70)( 67, 69)( 71, 72)
( 73, 77)( 74, 76)( 78, 79)( 80, 84)( 81, 83)( 85, 86)( 87, 91)( 88, 90)
( 92, 93)( 94, 98)( 95, 97)( 99,100)(101,105)(102,104)(106,107)(108,112)
(109,111)(113,114)(115,119)(116,118)(120,121)(122,126)(123,125)(127,128)
(129,133)(130,132)(134,135)(136,140)(137,139);
poly := sub<Sym(140)|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, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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 >; 
 
References : None.
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