Polytope of Type {7,14,6}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope