Polytope of Type {6,14,7}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,14,7}*1176
if this polytope has a name.
Group : SmallGroup(1176,237)
Rank : 4
Schlafli Type : {6,14,7}
Number of vertices, edges, etc : 6, 42, 49, 7
Order of s₀s₁s₂s₃ : 42
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) :
   3-fold quotients : {2,14,7}*392
   7-fold quotients : {6,2,7}*168
   14-fold quotients : {3,2,7}*84
   21-fold quotients : {2,2,7}*56
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 50, 99)( 51,100)( 52,101)( 53,102)( 54,103)( 55,104)( 56,105)( 57,106)
( 58,107)( 59,108)( 60,109)( 61,110)( 62,111)( 63,112)( 64,113)( 65,114)
( 66,115)( 67,116)( 68,117)( 69,118)( 70,119)( 71,120)( 72,121)( 73,122)
( 74,123)( 75,124)( 76,125)( 77,126)( 78,127)( 79,128)( 80,129)( 81,130)
( 82,131)( 83,132)( 84,133)( 85,134)( 86,135)( 87,136)( 88,137)( 89,138)
( 90,139)( 91,140)( 92,141)( 93,142)( 94,143)( 95,144)( 96,145)( 97,146)
( 98,147);;
s1 := (  1, 50)(  2, 51)(  3, 52)(  4, 53)(  5, 54)(  6, 55)(  7, 56)(  8, 92)
(  9, 93)( 10, 94)( 11, 95)( 12, 96)( 13, 97)( 14, 98)( 15, 85)( 16, 86)
( 17, 87)( 18, 88)( 19, 89)( 20, 90)( 21, 91)( 22, 78)( 23, 79)( 24, 80)
( 25, 81)( 26, 82)( 27, 83)( 28, 84)( 29, 71)( 30, 72)( 31, 73)( 32, 74)
( 33, 75)( 34, 76)( 35, 77)( 36, 64)( 37, 65)( 38, 66)( 39, 67)( 40, 68)
( 41, 69)( 42, 70)( 43, 57)( 44, 58)( 45, 59)( 46, 60)( 47, 61)( 48, 62)
( 49, 63)(106,141)(107,142)(108,143)(109,144)(110,145)(111,146)(112,147)
(113,134)(114,135)(115,136)(116,137)(117,138)(118,139)(119,140)(120,127)
(121,128)(122,129)(123,130)(124,131)(125,132)(126,133);;
s2 := (  1,  8)(  2, 14)(  3, 13)(  4, 12)(  5, 11)(  6, 10)(  7,  9)( 15, 43)
( 16, 49)( 17, 48)( 18, 47)( 19, 46)( 20, 45)( 21, 44)( 22, 36)( 23, 42)
( 24, 41)( 25, 40)( 26, 39)( 27, 38)( 28, 37)( 30, 35)( 31, 34)( 32, 33)
( 50, 57)( 51, 63)( 52, 62)( 53, 61)( 54, 60)( 55, 59)( 56, 58)( 64, 92)
( 65, 98)( 66, 97)( 67, 96)( 68, 95)( 69, 94)( 70, 93)( 71, 85)( 72, 91)
( 73, 90)( 74, 89)( 75, 88)( 76, 87)( 77, 86)( 79, 84)( 80, 83)( 81, 82)
( 99,106)(100,112)(101,111)(102,110)(103,109)(104,108)(105,107)(113,141)
(114,147)(115,146)(116,145)(117,144)(118,143)(119,142)(120,134)(121,140)
(122,139)(123,138)(124,137)(125,136)(126,135)(128,133)(129,132)(130,131);;
s3 := (  1,  2)(  3,  7)(  4,  6)(  8, 44)(  9, 43)( 10, 49)( 11, 48)( 12, 47)
( 13, 46)( 14, 45)( 15, 37)( 16, 36)( 17, 42)( 18, 41)( 19, 40)( 20, 39)
( 21, 38)( 22, 30)( 23, 29)( 24, 35)( 25, 34)( 26, 33)( 27, 32)( 28, 31)
( 50, 51)( 52, 56)( 53, 55)( 57, 93)( 58, 92)( 59, 98)( 60, 97)( 61, 96)
( 62, 95)( 63, 94)( 64, 86)( 65, 85)( 66, 91)( 67, 90)( 68, 89)( 69, 88)
( 70, 87)( 71, 79)( 72, 78)( 73, 84)( 74, 83)( 75, 82)( 76, 81)( 77, 80)
( 99,100)(101,105)(102,104)(106,142)(107,141)(108,147)(109,146)(110,145)
(111,144)(112,143)(113,135)(114,134)(115,140)(116,139)(117,138)(118,137)
(119,136)(120,128)(121,127)(122,133)(123,132)(124,131)(125,130)(126,129);;
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, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(147)!( 50, 99)( 51,100)( 52,101)( 53,102)( 54,103)( 55,104)( 56,105)
( 57,106)( 58,107)( 59,108)( 60,109)( 61,110)( 62,111)( 63,112)( 64,113)
( 65,114)( 66,115)( 67,116)( 68,117)( 69,118)( 70,119)( 71,120)( 72,121)
( 73,122)( 74,123)( 75,124)( 76,125)( 77,126)( 78,127)( 79,128)( 80,129)
( 81,130)( 82,131)( 83,132)( 84,133)( 85,134)( 86,135)( 87,136)( 88,137)
( 89,138)( 90,139)( 91,140)( 92,141)( 93,142)( 94,143)( 95,144)( 96,145)
( 97,146)( 98,147);
s1 := Sym(147)!(  1, 50)(  2, 51)(  3, 52)(  4, 53)(  5, 54)(  6, 55)(  7, 56)
(  8, 92)(  9, 93)( 10, 94)( 11, 95)( 12, 96)( 13, 97)( 14, 98)( 15, 85)
( 16, 86)( 17, 87)( 18, 88)( 19, 89)( 20, 90)( 21, 91)( 22, 78)( 23, 79)
( 24, 80)( 25, 81)( 26, 82)( 27, 83)( 28, 84)( 29, 71)( 30, 72)( 31, 73)
( 32, 74)( 33, 75)( 34, 76)( 35, 77)( 36, 64)( 37, 65)( 38, 66)( 39, 67)
( 40, 68)( 41, 69)( 42, 70)( 43, 57)( 44, 58)( 45, 59)( 46, 60)( 47, 61)
( 48, 62)( 49, 63)(106,141)(107,142)(108,143)(109,144)(110,145)(111,146)
(112,147)(113,134)(114,135)(115,136)(116,137)(117,138)(118,139)(119,140)
(120,127)(121,128)(122,129)(123,130)(124,131)(125,132)(126,133);
s2 := Sym(147)!(  1,  8)(  2, 14)(  3, 13)(  4, 12)(  5, 11)(  6, 10)(  7,  9)
( 15, 43)( 16, 49)( 17, 48)( 18, 47)( 19, 46)( 20, 45)( 21, 44)( 22, 36)
( 23, 42)( 24, 41)( 25, 40)( 26, 39)( 27, 38)( 28, 37)( 30, 35)( 31, 34)
( 32, 33)( 50, 57)( 51, 63)( 52, 62)( 53, 61)( 54, 60)( 55, 59)( 56, 58)
( 64, 92)( 65, 98)( 66, 97)( 67, 96)( 68, 95)( 69, 94)( 70, 93)( 71, 85)
( 72, 91)( 73, 90)( 74, 89)( 75, 88)( 76, 87)( 77, 86)( 79, 84)( 80, 83)
( 81, 82)( 99,106)(100,112)(101,111)(102,110)(103,109)(104,108)(105,107)
(113,141)(114,147)(115,146)(116,145)(117,144)(118,143)(119,142)(120,134)
(121,140)(122,139)(123,138)(124,137)(125,136)(126,135)(128,133)(129,132)
(130,131);
s3 := Sym(147)!(  1,  2)(  3,  7)(  4,  6)(  8, 44)(  9, 43)( 10, 49)( 11, 48)
( 12, 47)( 13, 46)( 14, 45)( 15, 37)( 16, 36)( 17, 42)( 18, 41)( 19, 40)
( 20, 39)( 21, 38)( 22, 30)( 23, 29)( 24, 35)( 25, 34)( 26, 33)( 27, 32)
( 28, 31)( 50, 51)( 52, 56)( 53, 55)( 57, 93)( 58, 92)( 59, 98)( 60, 97)
( 61, 96)( 62, 95)( 63, 94)( 64, 86)( 65, 85)( 66, 91)( 67, 90)( 68, 89)
( 69, 88)( 70, 87)( 71, 79)( 72, 78)( 73, 84)( 74, 83)( 75, 82)( 76, 81)
( 77, 80)( 99,100)(101,105)(102,104)(106,142)(107,141)(108,147)(109,146)
(110,145)(111,144)(112,143)(113,135)(114,134)(115,140)(116,139)(117,138)
(118,137)(119,136)(120,128)(121,127)(122,133)(123,132)(124,131)(125,130)
(126,129);
poly := sub<Sym(147)|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, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

References : None.
to this polytope