Polytope of Type {8,6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,6,6}*1152e
if this polytope has a name.
Group : SmallGroup(1152,157621)
Rank : 4
Schlafli Type : {8,6,6}
Number of vertices, edges, etc : 16, 48, 36, 6
Order of s₀s₁s₂s₃ : 6
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 : {4,6,6}*576b
   3-fold quotients : {8,6,2}*384c
   4-fold quotients : {4,3,6}*288, {4,6,6}*288e, {4,6,6}*288f
   6-fold quotients : {4,6,2}*192
   8-fold quotients : {4,3,6}*144, {2,6,6}*144c
   12-fold quotients : {4,3,2}*96, {4,6,2}*96b, {4,6,2}*96c
   16-fold quotients : {2,3,6}*72
   24-fold quotients : {4,3,2}*48, {2,6,2}*48
   48-fold quotients : {2,3,2}*24
   72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope