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Polytope of Type {12,66}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,66}*1584d
if this polytope has a name.
Group : SmallGroup(1584,662)
Rank : 3
Schlafli Type : {12,66}
Number of vertices, edges, etc : 12, 396, 66
Order of s0s1s2 : 33
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-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 : {4,66}*528c
   6-fold quotients : {4,33}*264
   11-fold quotients : {12,6}*144d
   33-fold quotients : {4,6}*48b
   66-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,  3)(  2,  4)(  5,  7)(  6,  8)(  9, 11)( 10, 12)( 13, 15)( 14, 16)
( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)
( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 91)( 46, 92)
( 47, 89)( 48, 90)( 49, 95)( 50, 96)( 51, 93)( 52, 94)( 53, 99)( 54,100)
( 55, 97)( 56, 98)( 57,103)( 58,104)( 59,101)( 60,102)( 61,107)( 62,108)
( 63,105)( 64,106)( 65,111)( 66,112)( 67,109)( 68,110)( 69,115)( 70,116)
( 71,113)( 72,114)( 73,119)( 74,120)( 75,117)( 76,118)( 77,123)( 78,124)
( 79,121)( 80,122)( 81,127)( 82,128)( 83,125)( 84,126)( 85,131)( 86,132)
( 87,129)( 88,130);;
s1 := (  1, 45)(  2, 46)(  3, 48)(  4, 47)(  5, 85)(  6, 86)(  7, 88)(  8, 87)
(  9, 81)( 10, 82)( 11, 84)( 12, 83)( 13, 77)( 14, 78)( 15, 80)( 16, 79)
( 17, 73)( 18, 74)( 19, 76)( 20, 75)( 21, 69)( 22, 70)( 23, 72)( 24, 71)
( 25, 65)( 26, 66)( 27, 68)( 28, 67)( 29, 61)( 30, 62)( 31, 64)( 32, 63)
( 33, 57)( 34, 58)( 35, 60)( 36, 59)( 37, 53)( 38, 54)( 39, 56)( 40, 55)
( 41, 49)( 42, 50)( 43, 52)( 44, 51)( 91, 92)( 93,129)( 94,130)( 95,132)
( 96,131)( 97,125)( 98,126)( 99,128)(100,127)(101,121)(102,122)(103,124)
(104,123)(105,117)(106,118)(107,120)(108,119)(109,113)(110,114)(111,116)
(112,115);;
s2 := (  1,  5)(  2,  8)(  3,  7)(  4,  6)(  9, 41)( 10, 44)( 11, 43)( 12, 42)
( 13, 37)( 14, 40)( 15, 39)( 16, 38)( 17, 33)( 18, 36)( 19, 35)( 20, 34)
( 21, 29)( 22, 32)( 23, 31)( 24, 30)( 26, 28)( 45, 49)( 46, 52)( 47, 51)
( 48, 50)( 53, 85)( 54, 88)( 55, 87)( 56, 86)( 57, 81)( 58, 84)( 59, 83)
( 60, 82)( 61, 77)( 62, 80)( 63, 79)( 64, 78)( 65, 73)( 66, 76)( 67, 75)
( 68, 74)( 70, 72)( 89, 93)( 90, 96)( 91, 95)( 92, 94)( 97,129)( 98,132)
( 99,131)(100,130)(101,125)(102,128)(103,127)(104,126)(105,121)(106,124)
(107,123)(108,122)(109,117)(110,120)(111,119)(112,118)(114,116);;
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*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(132)!(  1,  3)(  2,  4)(  5,  7)(  6,  8)(  9, 11)( 10, 12)( 13, 15)
( 14, 16)( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)
( 30, 32)( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 91)
( 46, 92)( 47, 89)( 48, 90)( 49, 95)( 50, 96)( 51, 93)( 52, 94)( 53, 99)
( 54,100)( 55, 97)( 56, 98)( 57,103)( 58,104)( 59,101)( 60,102)( 61,107)
( 62,108)( 63,105)( 64,106)( 65,111)( 66,112)( 67,109)( 68,110)( 69,115)
( 70,116)( 71,113)( 72,114)( 73,119)( 74,120)( 75,117)( 76,118)( 77,123)
( 78,124)( 79,121)( 80,122)( 81,127)( 82,128)( 83,125)( 84,126)( 85,131)
( 86,132)( 87,129)( 88,130);
s1 := Sym(132)!(  1, 45)(  2, 46)(  3, 48)(  4, 47)(  5, 85)(  6, 86)(  7, 88)
(  8, 87)(  9, 81)( 10, 82)( 11, 84)( 12, 83)( 13, 77)( 14, 78)( 15, 80)
( 16, 79)( 17, 73)( 18, 74)( 19, 76)( 20, 75)( 21, 69)( 22, 70)( 23, 72)
( 24, 71)( 25, 65)( 26, 66)( 27, 68)( 28, 67)( 29, 61)( 30, 62)( 31, 64)
( 32, 63)( 33, 57)( 34, 58)( 35, 60)( 36, 59)( 37, 53)( 38, 54)( 39, 56)
( 40, 55)( 41, 49)( 42, 50)( 43, 52)( 44, 51)( 91, 92)( 93,129)( 94,130)
( 95,132)( 96,131)( 97,125)( 98,126)( 99,128)(100,127)(101,121)(102,122)
(103,124)(104,123)(105,117)(106,118)(107,120)(108,119)(109,113)(110,114)
(111,116)(112,115);
s2 := Sym(132)!(  1,  5)(  2,  8)(  3,  7)(  4,  6)(  9, 41)( 10, 44)( 11, 43)
( 12, 42)( 13, 37)( 14, 40)( 15, 39)( 16, 38)( 17, 33)( 18, 36)( 19, 35)
( 20, 34)( 21, 29)( 22, 32)( 23, 31)( 24, 30)( 26, 28)( 45, 49)( 46, 52)
( 47, 51)( 48, 50)( 53, 85)( 54, 88)( 55, 87)( 56, 86)( 57, 81)( 58, 84)
( 59, 83)( 60, 82)( 61, 77)( 62, 80)( 63, 79)( 64, 78)( 65, 73)( 66, 76)
( 67, 75)( 68, 74)( 70, 72)( 89, 93)( 90, 96)( 91, 95)( 92, 94)( 97,129)
( 98,132)( 99,131)(100,130)(101,125)(102,128)(103,127)(104,126)(105,121)
(106,124)(107,123)(108,122)(109,117)(110,120)(111,119)(112,118)(114,116);
poly := sub<Sym(132)|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*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 
References : None.
to this polytope