Polytope of Type {2,6,6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,6,6}*1152b
if this polytope has a name.
Group : SmallGroup(1152,157863)
Rank : 5
Schlafli Type : {2,6,6,6}
Number of vertices, edges, etc : 2, 8, 24, 24, 6
Order of s₀s₁s₂s₃s₄ : 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   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 : {2,3,6,6}*576
   3-fold quotients : {2,6,6,2}*384
   6-fold quotients : {2,3,6,2}*192, {2,6,3,2}*192
   12-fold quotients : {2,3,3,2}*96, {2,2,2,6}*96
   24-fold quotients : {2,2,2,3}*48
   36-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4,  5)(  8,  9)( 12, 13)( 15, 27)( 16, 29)( 17, 28)( 18, 30)( 19, 31)
( 20, 33)( 21, 32)( 22, 34)( 23, 35)( 24, 37)( 25, 36)( 26, 38)( 40, 41)
( 44, 45)( 48, 49)( 51, 63)( 52, 65)( 53, 64)( 54, 66)( 55, 67)( 56, 69)
( 57, 68)( 58, 70)( 59, 71)( 60, 73)( 61, 72)( 62, 74)( 76, 77)( 80, 81)
( 84, 85)( 87, 99)( 88,101)( 89,100)( 90,102)( 91,103)( 92,105)( 93,104)
( 94,106)( 95,107)( 96,109)( 97,108)( 98,110)(112,113)(116,117)(120,121)
(123,135)(124,137)(125,136)(126,138)(127,139)(128,141)(129,140)(130,142)
(131,143)(132,145)(133,144)(134,146);;
s2 := (  3, 87)(  4, 88)(  5, 90)(  6, 89)(  7, 91)(  8, 92)(  9, 94)( 10, 93)
( 11, 95)( 12, 96)( 13, 98)( 14, 97)( 15, 75)( 16, 76)( 17, 78)( 18, 77)
( 19, 79)( 20, 80)( 21, 82)( 22, 81)( 23, 83)( 24, 84)( 25, 86)( 26, 85)
( 27, 99)( 28,100)( 29,102)( 30,101)( 31,103)( 32,104)( 33,106)( 34,105)
( 35,107)( 36,108)( 37,110)( 38,109)( 39,123)( 40,124)( 41,126)( 42,125)
( 43,127)( 44,128)( 45,130)( 46,129)( 47,131)( 48,132)( 49,134)( 50,133)
( 51,111)( 52,112)( 53,114)( 54,113)( 55,115)( 56,116)( 57,118)( 58,117)
( 59,119)( 60,120)( 61,122)( 62,121)( 63,135)( 64,136)( 65,138)( 66,137)
( 67,139)( 68,140)( 69,142)( 70,141)( 71,143)( 72,144)( 73,146)( 74,145);;
s3 := (  3,  6)(  7, 14)(  8, 12)(  9, 13)( 10, 11)( 15, 30)( 16, 28)( 17, 29)
( 18, 27)( 19, 38)( 20, 36)( 21, 37)( 22, 35)( 23, 34)( 24, 32)( 25, 33)
( 26, 31)( 39, 42)( 43, 50)( 44, 48)( 45, 49)( 46, 47)( 51, 66)( 52, 64)
( 53, 65)( 54, 63)( 55, 74)( 56, 72)( 57, 73)( 58, 71)( 59, 70)( 60, 68)
( 61, 69)( 62, 67)( 75, 78)( 79, 86)( 80, 84)( 81, 85)( 82, 83)( 87,102)
( 88,100)( 89,101)( 90, 99)( 91,110)( 92,108)( 93,109)( 94,107)( 95,106)
( 96,104)( 97,105)( 98,103)(111,114)(115,122)(116,120)(117,121)(118,119)
(123,138)(124,136)(125,137)(126,135)(127,146)(128,144)(129,145)(130,143)
(131,142)(132,140)(133,141)(134,139);;
s4 := (  3, 43)(  4, 44)(  5, 45)(  6, 46)(  7, 39)(  8, 40)(  9, 41)( 10, 42)
( 11, 47)( 12, 48)( 13, 49)( 14, 50)( 15, 55)( 16, 56)( 17, 57)( 18, 58)
( 19, 51)( 20, 52)( 21, 53)( 22, 54)( 23, 59)( 24, 60)( 25, 61)( 26, 62)
( 27, 67)( 28, 68)( 29, 69)( 30, 70)( 31, 63)( 32, 64)( 33, 65)( 34, 66)
( 35, 71)( 36, 72)( 37, 73)( 38, 74)( 75,115)( 76,116)( 77,117)( 78,118)
( 79,111)( 80,112)( 81,113)( 82,114)( 83,119)( 84,120)( 85,121)( 86,122)
( 87,127)( 88,128)( 89,129)( 90,130)( 91,123)( 92,124)( 93,125)( 94,126)
( 95,131)( 96,132)( 97,133)( 98,134)( 99,139)(100,140)(101,141)(102,142)
(103,135)(104,136)(105,137)(106,138)(107,143)(108,144)(109,145)(110,146);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*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, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(146)!(1,2);
s1 := Sym(146)!(  4,  5)(  8,  9)( 12, 13)( 15, 27)( 16, 29)( 17, 28)( 18, 30)
( 19, 31)( 20, 33)( 21, 32)( 22, 34)( 23, 35)( 24, 37)( 25, 36)( 26, 38)
( 40, 41)( 44, 45)( 48, 49)( 51, 63)( 52, 65)( 53, 64)( 54, 66)( 55, 67)
( 56, 69)( 57, 68)( 58, 70)( 59, 71)( 60, 73)( 61, 72)( 62, 74)( 76, 77)
( 80, 81)( 84, 85)( 87, 99)( 88,101)( 89,100)( 90,102)( 91,103)( 92,105)
( 93,104)( 94,106)( 95,107)( 96,109)( 97,108)( 98,110)(112,113)(116,117)
(120,121)(123,135)(124,137)(125,136)(126,138)(127,139)(128,141)(129,140)
(130,142)(131,143)(132,145)(133,144)(134,146);
s2 := Sym(146)!(  3, 87)(  4, 88)(  5, 90)(  6, 89)(  7, 91)(  8, 92)(  9, 94)
( 10, 93)( 11, 95)( 12, 96)( 13, 98)( 14, 97)( 15, 75)( 16, 76)( 17, 78)
( 18, 77)( 19, 79)( 20, 80)( 21, 82)( 22, 81)( 23, 83)( 24, 84)( 25, 86)
( 26, 85)( 27, 99)( 28,100)( 29,102)( 30,101)( 31,103)( 32,104)( 33,106)
( 34,105)( 35,107)( 36,108)( 37,110)( 38,109)( 39,123)( 40,124)( 41,126)
( 42,125)( 43,127)( 44,128)( 45,130)( 46,129)( 47,131)( 48,132)( 49,134)
( 50,133)( 51,111)( 52,112)( 53,114)( 54,113)( 55,115)( 56,116)( 57,118)
( 58,117)( 59,119)( 60,120)( 61,122)( 62,121)( 63,135)( 64,136)( 65,138)
( 66,137)( 67,139)( 68,140)( 69,142)( 70,141)( 71,143)( 72,144)( 73,146)
( 74,145);
s3 := Sym(146)!(  3,  6)(  7, 14)(  8, 12)(  9, 13)( 10, 11)( 15, 30)( 16, 28)
( 17, 29)( 18, 27)( 19, 38)( 20, 36)( 21, 37)( 22, 35)( 23, 34)( 24, 32)
( 25, 33)( 26, 31)( 39, 42)( 43, 50)( 44, 48)( 45, 49)( 46, 47)( 51, 66)
( 52, 64)( 53, 65)( 54, 63)( 55, 74)( 56, 72)( 57, 73)( 58, 71)( 59, 70)
( 60, 68)( 61, 69)( 62, 67)( 75, 78)( 79, 86)( 80, 84)( 81, 85)( 82, 83)
( 87,102)( 88,100)( 89,101)( 90, 99)( 91,110)( 92,108)( 93,109)( 94,107)
( 95,106)( 96,104)( 97,105)( 98,103)(111,114)(115,122)(116,120)(117,121)
(118,119)(123,138)(124,136)(125,137)(126,135)(127,146)(128,144)(129,145)
(130,143)(131,142)(132,140)(133,141)(134,139);
s4 := Sym(146)!(  3, 43)(  4, 44)(  5, 45)(  6, 46)(  7, 39)(  8, 40)(  9, 41)
( 10, 42)( 11, 47)( 12, 48)( 13, 49)( 14, 50)( 15, 55)( 16, 56)( 17, 57)
( 18, 58)( 19, 51)( 20, 52)( 21, 53)( 22, 54)( 23, 59)( 24, 60)( 25, 61)
( 26, 62)( 27, 67)( 28, 68)( 29, 69)( 30, 70)( 31, 63)( 32, 64)( 33, 65)
( 34, 66)( 35, 71)( 36, 72)( 37, 73)( 38, 74)( 75,115)( 76,116)( 77,117)
( 78,118)( 79,111)( 80,112)( 81,113)( 82,114)( 83,119)( 84,120)( 85,121)
( 86,122)( 87,127)( 88,128)( 89,129)( 90,130)( 91,123)( 92,124)( 93,125)
( 94,126)( 95,131)( 96,132)( 97,133)( 98,134)( 99,139)(100,140)(101,141)
(102,142)(103,135)(104,136)(105,137)(106,138)(107,143)(108,144)(109,145)
(110,146);
poly := sub<Sym(146)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*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, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope