Polytope of Type {6,33,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,33,4}*1584
if this polytope has a name.
Group : SmallGroup(1584,662)
Rank : 4
Schlafli Type : {6,33,4}
Number of vertices, edges, etc : 6, 99, 66, 4
Order of s₀s₁s₂s₃ : 66
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   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 : {2,33,4}*528
   11-fold quotients : {6,3,4}*144
   33-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 45, 89)( 46, 90)( 47, 91)( 48, 92)( 49, 93)( 50, 94)( 51, 95)( 52, 96)
( 53, 97)( 54, 98)( 55, 99)( 56,100)( 57,101)( 58,102)( 59,103)( 60,104)
( 61,105)( 62,106)( 63,107)( 64,108)( 65,109)( 66,110)( 67,111)( 68,112)
( 69,113)( 70,114)( 71,115)( 72,116)( 73,117)( 74,118)( 75,119)( 76,120)
( 77,121)( 78,122)( 79,123)( 80,124)( 81,125)( 82,126)( 83,127)( 84,128)
( 85,129)( 86,130)( 87,131)( 88,132);;
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, 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);;
s3 := (  1,  2)(  3,  4)(  5,  6)(  7,  8)(  9, 10)( 11, 12)( 13, 14)( 15, 16)
( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)
( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)
( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)
( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)
( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 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,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s2*s1*s3*s2*s3*s2*s1*s2, s2*s0*s1*s0*s1*s2*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*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)!( 45, 89)( 46, 90)( 47, 91)( 48, 92)( 49, 93)( 50, 94)( 51, 95)
( 52, 96)( 53, 97)( 54, 98)( 55, 99)( 56,100)( 57,101)( 58,102)( 59,103)
( 60,104)( 61,105)( 62,106)( 63,107)( 64,108)( 65,109)( 66,110)( 67,111)
( 68,112)( 69,113)( 70,114)( 71,115)( 72,116)( 73,117)( 74,118)( 75,119)
( 76,120)( 77,121)( 78,122)( 79,123)( 80,124)( 81,125)( 82,126)( 83,127)
( 84,128)( 85,129)( 86,130)( 87,131)( 88,132);
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, 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);
s3 := Sym(132)!(  1,  2)(  3,  4)(  5,  6)(  7,  8)(  9, 10)( 11, 12)( 13, 14)
( 15, 16)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)
( 31, 32)( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)
( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)
( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)
( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 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,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3, s3*s2*s1*s3*s2*s3*s2*s1*s2, 
s2*s0*s1*s0*s1*s2*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*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