Polytope of Type {14,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,12}*1176
if this polytope has a name.
Group : SmallGroup(1176,234)
Rank : 3
Schlafli Type : {14,12}
Number of vertices, edges, etc : 49, 294, 42
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 14
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
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 : {14,4}*392
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,  8)(  2,  9)(  3, 10)(  4, 11)(  5, 12)(  6, 13)(  7, 14)( 15, 43)
( 16, 44)( 17, 45)( 18, 46)( 19, 47)( 20, 48)( 21, 49)( 22, 36)( 23, 37)
( 24, 38)( 25, 39)( 26, 40)( 27, 41)( 28, 42)( 50,106)( 51,107)( 52,108)
( 53,109)( 54,110)( 55,111)( 56,112)( 57, 99)( 58,100)( 59,101)( 60,102)
( 61,103)( 62,104)( 63,105)( 64,141)( 65,142)( 66,143)( 67,144)( 68,145)
( 69,146)( 70,147)( 71,134)( 72,135)( 73,136)( 74,137)( 75,138)( 76,139)
( 77,140)( 78,127)( 79,128)( 80,129)( 81,130)( 82,131)( 83,132)( 84,133)
( 85,120)( 86,121)( 87,122)( 88,123)( 89,124)( 90,125)( 91,126)( 92,113)
( 93,114)( 94,115)( 95,116)( 96,117)( 97,118)( 98,119);;
s2 := (  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);;
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*s0*s1*s0*s1*s2*s1*s2*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, 
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*s2*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s2 ];;
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,  8)(  2,  9)(  3, 10)(  4, 11)(  5, 12)(  6, 13)(  7, 14)
( 15, 43)( 16, 44)( 17, 45)( 18, 46)( 19, 47)( 20, 48)( 21, 49)( 22, 36)
( 23, 37)( 24, 38)( 25, 39)( 26, 40)( 27, 41)( 28, 42)( 50,106)( 51,107)
( 52,108)( 53,109)( 54,110)( 55,111)( 56,112)( 57, 99)( 58,100)( 59,101)
( 60,102)( 61,103)( 62,104)( 63,105)( 64,141)( 65,142)( 66,143)( 67,144)
( 68,145)( 69,146)( 70,147)( 71,134)( 72,135)( 73,136)( 74,137)( 75,138)
( 76,139)( 77,140)( 78,127)( 79,128)( 80,129)( 81,130)( 82,131)( 83,132)
( 84,133)( 85,120)( 86,121)( 87,122)( 88,123)( 89,124)( 90,125)( 91,126)
( 92,113)( 93,114)( 94,115)( 95,116)( 96,117)( 97,118)( 98,119);
s2 := 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);
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*s0*s1*s0*s1*s2*s1*s2*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, 
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*s2*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s2 >;

References : None.
to this polytope