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

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

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