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Polytope of Type {2,6,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,6,4}*1152b
if this polytope has a name.
Group : SmallGroup(1152,157863)
Rank : 5
Schlafli Type : {2,6,6,4}
Number of vertices, edges, etc : 2, 6, 36, 24, 8
Order of s0s1s2s3s4 : 6
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 : {2,6,3,4}*576, {2,6,6,4}*576e, {2,6,6,4}*576f
   3-fold quotients : {2,2,6,4}*384
   4-fold quotients : {2,6,3,4}*288, {2,6,6,2}*288b
   6-fold quotients : {2,2,3,4}*192, {2,2,6,4}*192b, {2,2,6,4}*192c
   8-fold quotients : {2,6,3,2}*144
   12-fold quotients : {2,2,3,4}*96, {2,2,6,2}*96
   24-fold quotients : {2,2,3,2}*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 := (  7, 11)(  8, 12)(  9, 13)( 10, 14)( 19, 23)( 20, 24)( 21, 25)( 22, 26)
( 31, 35)( 32, 36)( 33, 37)( 34, 38)( 43, 47)( 44, 48)( 45, 49)( 46, 50)
( 55, 59)( 56, 60)( 57, 61)( 58, 62)( 67, 71)( 68, 72)( 69, 73)( 70, 74)
( 79, 83)( 80, 84)( 81, 85)( 82, 86)( 91, 95)( 92, 96)( 93, 97)( 94, 98)
(103,107)(104,108)(105,109)(106,110)(115,119)(116,120)(117,121)(118,122)
(127,131)(128,132)(129,133)(130,134)(139,143)(140,144)(141,145)(142,146);;
s2 := (  3,  7)(  4,  9)(  5,  8)(  6, 10)( 12, 13)( 15, 31)( 16, 33)( 17, 32)
( 18, 34)( 19, 27)( 20, 29)( 21, 28)( 22, 30)( 23, 35)( 24, 37)( 25, 36)
( 26, 38)( 39, 43)( 40, 45)( 41, 44)( 42, 46)( 48, 49)( 51, 67)( 52, 69)
( 53, 68)( 54, 70)( 55, 63)( 56, 65)( 57, 64)( 58, 66)( 59, 71)( 60, 73)
( 61, 72)( 62, 74)( 75, 79)( 76, 81)( 77, 80)( 78, 82)( 84, 85)( 87,103)
( 88,105)( 89,104)( 90,106)( 91, 99)( 92,101)( 93,100)( 94,102)( 95,107)
( 96,109)( 97,108)( 98,110)(111,115)(112,117)(113,116)(114,118)(120,121)
(123,139)(124,141)(125,140)(126,142)(127,135)(128,137)(129,136)(130,138)
(131,143)(132,145)(133,144)(134,146);;
s3 := (  3, 87)(  4, 88)(  5, 90)(  6, 89)(  7, 95)(  8, 96)(  9, 98)( 10, 97)
( 11, 91)( 12, 92)( 13, 94)( 14, 93)( 15, 75)( 16, 76)( 17, 78)( 18, 77)
( 19, 83)( 20, 84)( 21, 86)( 22, 85)( 23, 79)( 24, 80)( 25, 82)( 26, 81)
( 27, 99)( 28,100)( 29,102)( 30,101)( 31,107)( 32,108)( 33,110)( 34,109)
( 35,103)( 36,104)( 37,106)( 38,105)( 39,123)( 40,124)( 41,126)( 42,125)
( 43,131)( 44,132)( 45,134)( 46,133)( 47,127)( 48,128)( 49,130)( 50,129)
( 51,111)( 52,112)( 53,114)( 54,113)( 55,119)( 56,120)( 57,122)( 58,121)
( 59,115)( 60,116)( 61,118)( 62,117)( 63,135)( 64,136)( 65,138)( 66,137)
( 67,143)( 68,144)( 69,146)( 70,145)( 71,139)( 72,140)( 73,142)( 74,141);;
s4 := (  3, 42)(  4, 41)(  5, 40)(  6, 39)(  7, 46)(  8, 45)(  9, 44)( 10, 43)
( 11, 50)( 12, 49)( 13, 48)( 14, 47)( 15, 54)( 16, 53)( 17, 52)( 18, 51)
( 19, 58)( 20, 57)( 21, 56)( 22, 55)( 23, 62)( 24, 61)( 25, 60)( 26, 59)
( 27, 66)( 28, 65)( 29, 64)( 30, 63)( 31, 70)( 32, 69)( 33, 68)( 34, 67)
( 35, 74)( 36, 73)( 37, 72)( 38, 71)( 75,114)( 76,113)( 77,112)( 78,111)
( 79,118)( 80,117)( 81,116)( 82,115)( 83,122)( 84,121)( 85,120)( 86,119)
( 87,126)( 88,125)( 89,124)( 90,123)( 91,130)( 92,129)( 93,128)( 94,127)
( 95,134)( 96,133)( 97,132)( 98,131)( 99,138)(100,137)(101,136)(102,135)
(103,142)(104,141)(105,140)(106,139)(107,146)(108,145)(109,144)(110,143);;
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, 
s3*s4*s3*s4*s3*s4*s3*s4, s3*s1*s2*s1*s2*s3*s1*s2*s1*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*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(146)!(1,2);
s1 := Sym(146)!(  7, 11)(  8, 12)(  9, 13)( 10, 14)( 19, 23)( 20, 24)( 21, 25)
( 22, 26)( 31, 35)( 32, 36)( 33, 37)( 34, 38)( 43, 47)( 44, 48)( 45, 49)
( 46, 50)( 55, 59)( 56, 60)( 57, 61)( 58, 62)( 67, 71)( 68, 72)( 69, 73)
( 70, 74)( 79, 83)( 80, 84)( 81, 85)( 82, 86)( 91, 95)( 92, 96)( 93, 97)
( 94, 98)(103,107)(104,108)(105,109)(106,110)(115,119)(116,120)(117,121)
(118,122)(127,131)(128,132)(129,133)(130,134)(139,143)(140,144)(141,145)
(142,146);
s2 := Sym(146)!(  3,  7)(  4,  9)(  5,  8)(  6, 10)( 12, 13)( 15, 31)( 16, 33)
( 17, 32)( 18, 34)( 19, 27)( 20, 29)( 21, 28)( 22, 30)( 23, 35)( 24, 37)
( 25, 36)( 26, 38)( 39, 43)( 40, 45)( 41, 44)( 42, 46)( 48, 49)( 51, 67)
( 52, 69)( 53, 68)( 54, 70)( 55, 63)( 56, 65)( 57, 64)( 58, 66)( 59, 71)
( 60, 73)( 61, 72)( 62, 74)( 75, 79)( 76, 81)( 77, 80)( 78, 82)( 84, 85)
( 87,103)( 88,105)( 89,104)( 90,106)( 91, 99)( 92,101)( 93,100)( 94,102)
( 95,107)( 96,109)( 97,108)( 98,110)(111,115)(112,117)(113,116)(114,118)
(120,121)(123,139)(124,141)(125,140)(126,142)(127,135)(128,137)(129,136)
(130,138)(131,143)(132,145)(133,144)(134,146);
s3 := Sym(146)!(  3, 87)(  4, 88)(  5, 90)(  6, 89)(  7, 95)(  8, 96)(  9, 98)
( 10, 97)( 11, 91)( 12, 92)( 13, 94)( 14, 93)( 15, 75)( 16, 76)( 17, 78)
( 18, 77)( 19, 83)( 20, 84)( 21, 86)( 22, 85)( 23, 79)( 24, 80)( 25, 82)
( 26, 81)( 27, 99)( 28,100)( 29,102)( 30,101)( 31,107)( 32,108)( 33,110)
( 34,109)( 35,103)( 36,104)( 37,106)( 38,105)( 39,123)( 40,124)( 41,126)
( 42,125)( 43,131)( 44,132)( 45,134)( 46,133)( 47,127)( 48,128)( 49,130)
( 50,129)( 51,111)( 52,112)( 53,114)( 54,113)( 55,119)( 56,120)( 57,122)
( 58,121)( 59,115)( 60,116)( 61,118)( 62,117)( 63,135)( 64,136)( 65,138)
( 66,137)( 67,143)( 68,144)( 69,146)( 70,145)( 71,139)( 72,140)( 73,142)
( 74,141);
s4 := Sym(146)!(  3, 42)(  4, 41)(  5, 40)(  6, 39)(  7, 46)(  8, 45)(  9, 44)
( 10, 43)( 11, 50)( 12, 49)( 13, 48)( 14, 47)( 15, 54)( 16, 53)( 17, 52)
( 18, 51)( 19, 58)( 20, 57)( 21, 56)( 22, 55)( 23, 62)( 24, 61)( 25, 60)
( 26, 59)( 27, 66)( 28, 65)( 29, 64)( 30, 63)( 31, 70)( 32, 69)( 33, 68)
( 34, 67)( 35, 74)( 36, 73)( 37, 72)( 38, 71)( 75,114)( 76,113)( 77,112)
( 78,111)( 79,118)( 80,117)( 81,116)( 82,115)( 83,122)( 84,121)( 85,120)
( 86,119)( 87,126)( 88,125)( 89,124)( 90,123)( 91,130)( 92,129)( 93,128)
( 94,127)( 95,134)( 96,133)( 97,132)( 98,131)( 99,138)(100,137)(101,136)
(102,135)(103,142)(104,141)(105,140)(106,139)(107,146)(108,145)(109,144)
(110,143);
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, s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*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*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3 >; 
 

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