Polytope of Type {6,6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6,6}*1152a
if this polytope has a name.
Group : SmallGroup(1152,157621)
Rank : 4
Schlafli Type : {6,6,6}
Number of vertices, edges, etc : 6, 48, 48, 16
Order of s₀s₁s₂s₃ : 24
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   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) :
   2-fold quotients : {6,6,6}*576a
   3-fold quotients : {2,6,6}*384b
   4-fold quotients : {6,6,3}*288
   6-fold quotients : {2,6,6}*192
   12-fold quotients : {2,3,6}*96, {2,6,3}*96
   24-fold quotients : {2,3,3}*48, {6,2,2}*48
   48-fold quotients : {3,2,2}*24
   72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  9, 17)( 10, 18)( 11, 19)( 12, 20)( 13, 21)( 14, 22)( 15, 23)( 16, 24)
( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)
( 57, 65)( 58, 66)( 59, 67)( 60, 68)( 61, 69)( 62, 70)( 63, 71)( 64, 72)
( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)
(105,113)(106,114)(107,115)(108,116)(109,117)(110,118)(111,119)(112,120)
(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144);;
s1 := (  1,  9)(  2, 10)(  3, 12)(  4, 11)(  5, 15)(  6, 16)(  7, 13)(  8, 14)
( 19, 20)( 21, 23)( 22, 24)( 25, 57)( 26, 58)( 27, 60)( 28, 59)( 29, 63)
( 30, 64)( 31, 61)( 32, 62)( 33, 49)( 34, 50)( 35, 52)( 36, 51)( 37, 55)
( 38, 56)( 39, 53)( 40, 54)( 41, 65)( 42, 66)( 43, 68)( 44, 67)( 45, 71)
( 46, 72)( 47, 69)( 48, 70)( 73, 82)( 74, 81)( 75, 83)( 76, 84)( 77, 88)
( 78, 87)( 79, 86)( 80, 85)( 89, 90)( 93, 96)( 94, 95)( 97,130)( 98,129)
( 99,131)(100,132)(101,136)(102,135)(103,134)(104,133)(105,122)(106,121)
(107,123)(108,124)(109,128)(110,127)(111,126)(112,125)(113,138)(114,137)
(115,139)(116,140)(117,144)(118,143)(119,142)(120,141);;
s2 := (  1, 25)(  2, 26)(  3, 31)(  4, 32)(  5, 30)(  6, 29)(  7, 27)(  8, 28)
(  9, 33)( 10, 34)( 11, 39)( 12, 40)( 13, 38)( 14, 37)( 15, 35)( 16, 36)
( 17, 41)( 18, 42)( 19, 47)( 20, 48)( 21, 46)( 22, 45)( 23, 43)( 24, 44)
( 51, 55)( 52, 56)( 53, 54)( 59, 63)( 60, 64)( 61, 62)( 67, 71)( 68, 72)
( 69, 70)( 73, 97)( 74, 98)( 75,103)( 76,104)( 77,102)( 78,101)( 79, 99)
( 80,100)( 81,105)( 82,106)( 83,111)( 84,112)( 85,110)( 86,109)( 87,107)
( 88,108)( 89,113)( 90,114)( 91,119)( 92,120)( 93,118)( 94,117)( 95,115)
( 96,116)(123,127)(124,128)(125,126)(131,135)(132,136)(133,134)(139,143)
(140,144)(141,142);;
s3 := (  1, 75)(  2, 76)(  3, 73)(  4, 74)(  5, 78)(  6, 77)(  7, 79)(  8, 80)
(  9, 83)( 10, 84)( 11, 81)( 12, 82)( 13, 86)( 14, 85)( 15, 87)( 16, 88)
( 17, 91)( 18, 92)( 19, 89)( 20, 90)( 21, 94)( 22, 93)( 23, 95)( 24, 96)
( 25,123)( 26,124)( 27,121)( 28,122)( 29,126)( 30,125)( 31,127)( 32,128)
( 33,131)( 34,132)( 35,129)( 36,130)( 37,134)( 38,133)( 39,135)( 40,136)
( 41,139)( 42,140)( 43,137)( 44,138)( 45,142)( 46,141)( 47,143)( 48,144)
( 49, 99)( 50,100)( 51, 97)( 52, 98)( 53,102)( 54,101)( 55,103)( 56,104)
( 57,107)( 58,108)( 59,105)( 60,106)( 61,110)( 62,109)( 63,111)( 64,112)
( 65,115)( 66,116)( 67,113)( 68,114)( 69,118)( 70,117)( 71,119)( 72,120);;
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, s0*s1*s2*s1*s0*s1*s2*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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s1*s2*s3*s2*s3*s1*s2*s3*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(144)!(  9, 17)( 10, 18)( 11, 19)( 12, 20)( 13, 21)( 14, 22)( 15, 23)
( 16, 24)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)
( 40, 48)( 57, 65)( 58, 66)( 59, 67)( 60, 68)( 61, 69)( 62, 70)( 63, 71)
( 64, 72)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)
( 88, 96)(105,113)(106,114)(107,115)(108,116)(109,117)(110,118)(111,119)
(112,120)(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)
(136,144);
s1 := Sym(144)!(  1,  9)(  2, 10)(  3, 12)(  4, 11)(  5, 15)(  6, 16)(  7, 13)
(  8, 14)( 19, 20)( 21, 23)( 22, 24)( 25, 57)( 26, 58)( 27, 60)( 28, 59)
( 29, 63)( 30, 64)( 31, 61)( 32, 62)( 33, 49)( 34, 50)( 35, 52)( 36, 51)
( 37, 55)( 38, 56)( 39, 53)( 40, 54)( 41, 65)( 42, 66)( 43, 68)( 44, 67)
( 45, 71)( 46, 72)( 47, 69)( 48, 70)( 73, 82)( 74, 81)( 75, 83)( 76, 84)
( 77, 88)( 78, 87)( 79, 86)( 80, 85)( 89, 90)( 93, 96)( 94, 95)( 97,130)
( 98,129)( 99,131)(100,132)(101,136)(102,135)(103,134)(104,133)(105,122)
(106,121)(107,123)(108,124)(109,128)(110,127)(111,126)(112,125)(113,138)
(114,137)(115,139)(116,140)(117,144)(118,143)(119,142)(120,141);
s2 := Sym(144)!(  1, 25)(  2, 26)(  3, 31)(  4, 32)(  5, 30)(  6, 29)(  7, 27)
(  8, 28)(  9, 33)( 10, 34)( 11, 39)( 12, 40)( 13, 38)( 14, 37)( 15, 35)
( 16, 36)( 17, 41)( 18, 42)( 19, 47)( 20, 48)( 21, 46)( 22, 45)( 23, 43)
( 24, 44)( 51, 55)( 52, 56)( 53, 54)( 59, 63)( 60, 64)( 61, 62)( 67, 71)
( 68, 72)( 69, 70)( 73, 97)( 74, 98)( 75,103)( 76,104)( 77,102)( 78,101)
( 79, 99)( 80,100)( 81,105)( 82,106)( 83,111)( 84,112)( 85,110)( 86,109)
( 87,107)( 88,108)( 89,113)( 90,114)( 91,119)( 92,120)( 93,118)( 94,117)
( 95,115)( 96,116)(123,127)(124,128)(125,126)(131,135)(132,136)(133,134)
(139,143)(140,144)(141,142);
s3 := Sym(144)!(  1, 75)(  2, 76)(  3, 73)(  4, 74)(  5, 78)(  6, 77)(  7, 79)
(  8, 80)(  9, 83)( 10, 84)( 11, 81)( 12, 82)( 13, 86)( 14, 85)( 15, 87)
( 16, 88)( 17, 91)( 18, 92)( 19, 89)( 20, 90)( 21, 94)( 22, 93)( 23, 95)
( 24, 96)( 25,123)( 26,124)( 27,121)( 28,122)( 29,126)( 30,125)( 31,127)
( 32,128)( 33,131)( 34,132)( 35,129)( 36,130)( 37,134)( 38,133)( 39,135)
( 40,136)( 41,139)( 42,140)( 43,137)( 44,138)( 45,142)( 46,141)( 47,143)
( 48,144)( 49, 99)( 50,100)( 51, 97)( 52, 98)( 53,102)( 54,101)( 55,103)
( 56,104)( 57,107)( 58,108)( 59,105)( 60,106)( 61,110)( 62,109)( 63,111)
( 64,112)( 65,115)( 66,116)( 67,113)( 68,114)( 69,118)( 70,117)( 71,119)
( 72,120);
poly := sub<Sym(144)|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, 
s0*s1*s2*s1*s0*s1*s2*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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s1*s2*s3*s2*s3*s1*s2*s3*s2*s1*s2 >;

References : None.
to this polytope