Polytope of Type {66,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {66,12}*1584d
if this polytope has a name.
Group : SmallGroup(1584,662)
Rank : 3
Schlafli Type : {66,12}
Number of vertices, edges, etc : 66, 396, 12
Order of s₀s₁s₂ : 33
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Flat
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 : {66,4}*528c
   6-fold quotients : {33,4}*264
   11-fold quotients : {6,12}*144d
   33-fold quotients : {6,4}*48b
   66-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope