Polytope of Type {14,42}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,42}*1176a
if this polytope has a name.
Group : SmallGroup(1176,237)
Rank : 3
Schlafli Type : {14,42}
Number of vertices, edges, etc : 14, 294, 42
Order of s₀s₁s₂ : 42
Order of s₀s₁s₂s₁ : 14
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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 : {14,14}*392c
   6-fold quotients : {7,14}*196
   7-fold quotients : {14,6}*168
   21-fold quotients : {14,2}*56
   42-fold quotients : {7,2}*28
   49-fold quotients : {2,6}*24
   98-fold quotients : {2,3}*12
   147-fold quotients : {2,2}*8
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)
( 50,107)( 51,106)( 52,112)( 53,111)( 54,110)( 55,109)( 56,108)( 57,100)
( 58, 99)( 59,105)( 60,104)( 61,103)( 62,102)( 63,101)( 64,142)( 65,141)
( 66,147)( 67,146)( 68,145)( 69,144)( 70,143)( 71,135)( 72,134)( 73,140)
( 74,139)( 75,138)( 76,137)( 77,136)( 78,128)( 79,127)( 80,133)( 81,132)
( 82,131)( 83,130)( 84,129)( 85,121)( 86,120)( 87,126)( 88,125)( 89,124)
( 90,123)( 91,122)( 92,114)( 93,113)( 94,119)( 95,118)( 96,117)( 97,116)
( 98,115);;
s2 := (  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);;
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*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(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)( 50,107)( 51,106)( 52,112)( 53,111)( 54,110)( 55,109)( 56,108)
( 57,100)( 58, 99)( 59,105)( 60,104)( 61,103)( 62,102)( 63,101)( 64,142)
( 65,141)( 66,147)( 67,146)( 68,145)( 69,144)( 70,143)( 71,135)( 72,134)
( 73,140)( 74,139)( 75,138)( 76,137)( 77,136)( 78,128)( 79,127)( 80,133)
( 81,132)( 82,131)( 83,130)( 84,129)( 85,121)( 86,120)( 87,126)( 88,125)
( 89,124)( 90,123)( 91,122)( 92,114)( 93,113)( 94,119)( 95,118)( 96,117)
( 97,116)( 98,115);
s2 := 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);
poly := sub<Sym(147)|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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*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.
to this polytope