Polytope of Type {12,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,14}*1176
if this polytope has a name.
Group : SmallGroup(1176,234)
Rank : 3
Schlafli Type : {12,14}
Number of vertices, edges, etc : 42, 294, 49
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 14
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {4,14}*392
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

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*s2*s0*s1*s2*s0*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, 
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, 
s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

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*s2*s0*s1*s2*s0*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, 
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, 
s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2 >;

References : None.
to this polytope