Polytope of Type {8,6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,6,6}*1152d
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}*576a
   3-fold quotients : {8,6,2}*384c
   4-fold quotients : {4,6,6}*288d
   6-fold quotients : {4,6,2}*192
   8-fold quotients : {2,6,6}*144a
   12-fold quotients : {4,3,2}*96, {4,6,2}*96b, {4,6,2}*96c
   24-fold quotients : {4,3,2}*48, {2,2,6}*48, {2,6,2}*48
   48-fold quotients : {2,2,3}*24, {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)( 11, 12)( 13, 15)( 14, 16)( 19, 20)( 21, 23)
( 22, 24)( 25, 49)( 26, 50)( 27, 52)( 28, 51)( 29, 55)( 30, 56)( 31, 53)
( 32, 54)( 33, 57)( 34, 58)( 35, 60)( 36, 59)( 37, 63)( 38, 64)( 39, 61)
( 40, 62)( 41, 65)( 42, 66)( 43, 68)( 44, 67)( 45, 71)( 46, 72)( 47, 69)
( 48, 70)( 75, 76)( 77, 79)( 78, 80)( 83, 84)( 85, 87)( 86, 88)( 91, 92)
( 93, 95)( 94, 96)( 97,121)( 98,122)( 99,124)(100,123)(101,127)(102,128)
(103,125)(104,126)(105,129)(106,130)(107,132)(108,131)(109,135)(110,136)
(111,133)(112,134)(113,137)(114,138)(115,140)(116,139)(117,143)(118,144)
(119,141)(120,142);;
s2 := (  1, 25)(  2, 26)(  3, 31)(  4, 32)(  5, 30)(  6, 29)(  7, 27)(  8, 28)
(  9, 41)( 10, 42)( 11, 47)( 12, 48)( 13, 46)( 14, 45)( 15, 43)( 16, 44)
( 17, 33)( 18, 34)( 19, 39)( 20, 40)( 21, 38)( 22, 37)( 23, 35)( 24, 36)
( 51, 55)( 52, 56)( 53, 54)( 57, 65)( 58, 66)( 59, 71)( 60, 72)( 61, 70)
( 62, 69)( 63, 67)( 64, 68)( 73, 98)( 74, 97)( 75,104)( 76,103)( 77,101)
( 78,102)( 79,100)( 80, 99)( 81,114)( 82,113)( 83,120)( 84,119)( 85,117)
( 86,118)( 87,116)( 88,115)( 89,106)( 90,105)( 91,112)( 92,111)( 93,109)
( 94,110)( 95,108)( 96,107)(121,122)(123,128)(124,127)(129,138)(130,137)
(131,144)(132,143)(133,141)(134,142)(135,140)(136,139);;
s3 := (  1,  9)(  2, 10)(  3, 11)(  4, 12)(  5, 13)(  6, 14)(  7, 15)(  8, 16)
( 25, 33)( 26, 34)( 27, 35)( 28, 36)( 29, 37)( 30, 38)( 31, 39)( 32, 40)
( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)( 56, 64)
( 73, 81)( 74, 82)( 75, 83)( 76, 84)( 77, 85)( 78, 86)( 79, 87)( 80, 88)
( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)
(121,129)(122,130)(123,131)(124,132)(125,133)(126,134)(127,135)(128,136);;
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, s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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)( 11, 12)( 13, 15)( 14, 16)( 19, 20)
( 21, 23)( 22, 24)( 25, 49)( 26, 50)( 27, 52)( 28, 51)( 29, 55)( 30, 56)
( 31, 53)( 32, 54)( 33, 57)( 34, 58)( 35, 60)( 36, 59)( 37, 63)( 38, 64)
( 39, 61)( 40, 62)( 41, 65)( 42, 66)( 43, 68)( 44, 67)( 45, 71)( 46, 72)
( 47, 69)( 48, 70)( 75, 76)( 77, 79)( 78, 80)( 83, 84)( 85, 87)( 86, 88)
( 91, 92)( 93, 95)( 94, 96)( 97,121)( 98,122)( 99,124)(100,123)(101,127)
(102,128)(103,125)(104,126)(105,129)(106,130)(107,132)(108,131)(109,135)
(110,136)(111,133)(112,134)(113,137)(114,138)(115,140)(116,139)(117,143)
(118,144)(119,141)(120,142);
s2 := Sym(144)!(  1, 25)(  2, 26)(  3, 31)(  4, 32)(  5, 30)(  6, 29)(  7, 27)
(  8, 28)(  9, 41)( 10, 42)( 11, 47)( 12, 48)( 13, 46)( 14, 45)( 15, 43)
( 16, 44)( 17, 33)( 18, 34)( 19, 39)( 20, 40)( 21, 38)( 22, 37)( 23, 35)
( 24, 36)( 51, 55)( 52, 56)( 53, 54)( 57, 65)( 58, 66)( 59, 71)( 60, 72)
( 61, 70)( 62, 69)( 63, 67)( 64, 68)( 73, 98)( 74, 97)( 75,104)( 76,103)
( 77,101)( 78,102)( 79,100)( 80, 99)( 81,114)( 82,113)( 83,120)( 84,119)
( 85,117)( 86,118)( 87,116)( 88,115)( 89,106)( 90,105)( 91,112)( 92,111)
( 93,109)( 94,110)( 95,108)( 96,107)(121,122)(123,128)(124,127)(129,138)
(130,137)(131,144)(132,143)(133,141)(134,142)(135,140)(136,139);
s3 := Sym(144)!(  1,  9)(  2, 10)(  3, 11)(  4, 12)(  5, 13)(  6, 14)(  7, 15)
(  8, 16)( 25, 33)( 26, 34)( 27, 35)( 28, 36)( 29, 37)( 30, 38)( 31, 39)
( 32, 40)( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)
( 56, 64)( 73, 81)( 74, 82)( 75, 83)( 76, 84)( 77, 85)( 78, 86)( 79, 87)
( 80, 88)( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)
(104,112)(121,129)(122,130)(123,131)(124,132)(125,133)(126,134)(127,135)
(128,136);
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, 
s1*s2*s3*s2*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1 >;

References : None.
to this polytope