Polytope of Type {14,4,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,4,10}*1120
Also Known As : {{14,4|2},{4,10|2}}. if this polytope has another name.
Group : SmallGroup(1120,998)
Rank : 4
Schlafli Type : {14,4,10}
Number of vertices, edges, etc : 14, 28, 20, 10
Order of s₀s₁s₂s₃ : 140
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   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 : {14,2,10}*560
   4-fold quotients : {7,2,10}*280, {14,2,5}*280
   5-fold quotients : {14,4,2}*224
   7-fold quotients : {2,4,10}*160
   8-fold quotients : {7,2,5}*140
   10-fold quotients : {14,2,2}*112
   14-fold quotients : {2,2,10}*80
   20-fold quotients : {7,2,2}*56
   28-fold quotients : {2,2,5}*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 := (  2,  7)(  3,  6)(  4,  5)(  9, 14)( 10, 13)( 11, 12)( 16, 21)( 17, 20)
( 18, 19)( 23, 28)( 24, 27)( 25, 26)( 30, 35)( 31, 34)( 32, 33)( 37, 42)
( 38, 41)( 39, 40)( 44, 49)( 45, 48)( 46, 47)( 51, 56)( 52, 55)( 53, 54)
( 58, 63)( 59, 62)( 60, 61)( 65, 70)( 66, 69)( 67, 68)( 72, 77)( 73, 76)
( 74, 75)( 79, 84)( 80, 83)( 81, 82)( 86, 91)( 87, 90)( 88, 89)( 93, 98)
( 94, 97)( 95, 96)(100,105)(101,104)(102,103)(107,112)(108,111)(109,110)
(114,119)(115,118)(116,117)(121,126)(122,125)(123,124)(128,133)(129,132)
(130,131)(135,140)(136,139)(137,138);;
s1 := (  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)( 71,107)( 72,106)
( 73,112)( 74,111)( 75,110)( 76,109)( 77,108)( 78,114)( 79,113)( 80,119)
( 81,118)( 82,117)( 83,116)( 84,115)( 85,121)( 86,120)( 87,126)( 88,125)
( 89,124)( 90,123)( 91,122)( 92,128)( 93,127)( 94,133)( 95,132)( 96,131)
( 97,130)( 98,129)( 99,135)(100,134)(101,140)(102,139)(103,138)(104,137)
(105,136);;
s2 := (  1, 71)(  2, 72)(  3, 73)(  4, 74)(  5, 75)(  6, 76)(  7, 77)(  8, 99)
(  9,100)( 10,101)( 11,102)( 12,103)( 13,104)( 14,105)( 15, 92)( 16, 93)
( 17, 94)( 18, 95)( 19, 96)( 20, 97)( 21, 98)( 22, 85)( 23, 86)( 24, 87)
( 25, 88)( 26, 89)( 27, 90)( 28, 91)( 29, 78)( 30, 79)( 31, 80)( 32, 81)
( 33, 82)( 34, 83)( 35, 84)( 36,106)( 37,107)( 38,108)( 39,109)( 40,110)
( 41,111)( 42,112)( 43,134)( 44,135)( 45,136)( 46,137)( 47,138)( 48,139)
( 49,140)( 50,127)( 51,128)( 52,129)( 53,130)( 54,131)( 55,132)( 56,133)
( 57,120)( 58,121)( 59,122)( 60,123)( 61,124)( 62,125)( 63,126)( 64,113)
( 65,114)( 66,115)( 67,116)( 68,117)( 69,118)( 70,119);;
s3 := (  1,  8)(  2,  9)(  3, 10)(  4, 11)(  5, 12)(  6, 13)(  7, 14)( 15, 29)
( 16, 30)( 17, 31)( 18, 32)( 19, 33)( 20, 34)( 21, 35)( 36, 43)( 37, 44)
( 38, 45)( 39, 46)( 40, 47)( 41, 48)( 42, 49)( 50, 64)( 51, 65)( 52, 66)
( 53, 67)( 54, 68)( 55, 69)( 56, 70)( 71, 78)( 72, 79)( 73, 80)( 74, 81)
( 75, 82)( 76, 83)( 77, 84)( 85, 99)( 86,100)( 87,101)( 88,102)( 89,103)
( 90,104)( 91,105)(106,113)(107,114)(108,115)(109,116)(110,117)(111,118)
(112,119)(120,134)(121,135)(122,136)(123,137)(124,138)(125,139)(126,140);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, 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, 
s0*s1*s0*s1*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)(  9, 14)( 10, 13)( 11, 12)( 16, 21)
( 17, 20)( 18, 19)( 23, 28)( 24, 27)( 25, 26)( 30, 35)( 31, 34)( 32, 33)
( 37, 42)( 38, 41)( 39, 40)( 44, 49)( 45, 48)( 46, 47)( 51, 56)( 52, 55)
( 53, 54)( 58, 63)( 59, 62)( 60, 61)( 65, 70)( 66, 69)( 67, 68)( 72, 77)
( 73, 76)( 74, 75)( 79, 84)( 80, 83)( 81, 82)( 86, 91)( 87, 90)( 88, 89)
( 93, 98)( 94, 97)( 95, 96)(100,105)(101,104)(102,103)(107,112)(108,111)
(109,110)(114,119)(115,118)(116,117)(121,126)(122,125)(123,124)(128,133)
(129,132)(130,131)(135,140)(136,139)(137,138);
s1 := 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)( 71,107)
( 72,106)( 73,112)( 74,111)( 75,110)( 76,109)( 77,108)( 78,114)( 79,113)
( 80,119)( 81,118)( 82,117)( 83,116)( 84,115)( 85,121)( 86,120)( 87,126)
( 88,125)( 89,124)( 90,123)( 91,122)( 92,128)( 93,127)( 94,133)( 95,132)
( 96,131)( 97,130)( 98,129)( 99,135)(100,134)(101,140)(102,139)(103,138)
(104,137)(105,136);
s2 := Sym(140)!(  1, 71)(  2, 72)(  3, 73)(  4, 74)(  5, 75)(  6, 76)(  7, 77)
(  8, 99)(  9,100)( 10,101)( 11,102)( 12,103)( 13,104)( 14,105)( 15, 92)
( 16, 93)( 17, 94)( 18, 95)( 19, 96)( 20, 97)( 21, 98)( 22, 85)( 23, 86)
( 24, 87)( 25, 88)( 26, 89)( 27, 90)( 28, 91)( 29, 78)( 30, 79)( 31, 80)
( 32, 81)( 33, 82)( 34, 83)( 35, 84)( 36,106)( 37,107)( 38,108)( 39,109)
( 40,110)( 41,111)( 42,112)( 43,134)( 44,135)( 45,136)( 46,137)( 47,138)
( 48,139)( 49,140)( 50,127)( 51,128)( 52,129)( 53,130)( 54,131)( 55,132)
( 56,133)( 57,120)( 58,121)( 59,122)( 60,123)( 61,124)( 62,125)( 63,126)
( 64,113)( 65,114)( 66,115)( 67,116)( 68,117)( 69,118)( 70,119);
s3 := Sym(140)!(  1,  8)(  2,  9)(  3, 10)(  4, 11)(  5, 12)(  6, 13)(  7, 14)
( 15, 29)( 16, 30)( 17, 31)( 18, 32)( 19, 33)( 20, 34)( 21, 35)( 36, 43)
( 37, 44)( 38, 45)( 39, 46)( 40, 47)( 41, 48)( 42, 49)( 50, 64)( 51, 65)
( 52, 66)( 53, 67)( 54, 68)( 55, 69)( 56, 70)( 71, 78)( 72, 79)( 73, 80)
( 74, 81)( 75, 82)( 76, 83)( 77, 84)( 85, 99)( 86,100)( 87,101)( 88,102)
( 89,103)( 90,104)( 91,105)(106,113)(107,114)(108,115)(109,116)(110,117)
(111,118)(112,119)(120,134)(121,135)(122,136)(123,137)(124,138)(125,139)
(126,140);
poly := sub<Sym(140)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
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, 
s0*s1*s0*s1*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.
to this polytope