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Polytope of Type {2,4,6,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,6,12}*1152d
if this polytope has a name.
Group : SmallGroup(1152,157550)
Rank : 5
Schlafli Type : {2,4,6,12}
Number of vertices, edges, etc : 2, 4, 12, 36, 12
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-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 : {2,4,6,4}*384c
   6-fold quotients : {2,4,6,2}*192c
   12-fold quotients : {2,4,3,2}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (  3,  5)(  4,  6)(  7,  9)(  8, 10)( 11, 13)( 12, 14)( 15, 17)( 16, 18)
( 19, 21)( 20, 22)( 23, 25)( 24, 26)( 27, 29)( 28, 30)( 31, 33)( 32, 34)
( 35, 37)( 36, 38)( 39, 41)( 40, 42)( 43, 45)( 44, 46)( 47, 49)( 48, 50)
( 51, 53)( 52, 54)( 55, 57)( 56, 58)( 59, 61)( 60, 62)( 63, 65)( 64, 66)
( 67, 69)( 68, 70)( 71, 73)( 72, 74)( 75, 77)( 76, 78)( 79, 81)( 80, 82)
( 83, 85)( 84, 86)( 87, 89)( 88, 90)( 91, 93)( 92, 94)( 95, 97)( 96, 98)
( 99,101)(100,102)(103,105)(104,106)(107,109)(108,110)(111,113)(112,114)
(115,117)(116,118)(119,121)(120,122)(123,125)(124,126)(127,129)(128,130)
(131,133)(132,134)(135,137)(136,138)(139,141)(140,142)(143,145)(144,146);;
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)( 75,135)( 76,138)( 77,137)( 78,136)( 79,143)( 80,146)
( 81,145)( 82,144)( 83,139)( 84,142)( 85,141)( 86,140)( 87,123)( 88,126)
( 89,125)( 90,124)( 91,131)( 92,134)( 93,133)( 94,132)( 95,127)( 96,130)
( 97,129)( 98,128)( 99,111)(100,114)(101,113)(102,112)(103,119)(104,122)
(105,121)(106,120)(107,115)(108,118)(109,117)(110,116);;
s4 := (  3, 79)(  4, 80)(  5, 81)(  6, 82)(  7, 75)(  8, 76)(  9, 77)( 10, 78)
( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 91)( 16, 92)( 17, 93)( 18, 94)
( 19, 87)( 20, 88)( 21, 89)( 22, 90)( 23, 95)( 24, 96)( 25, 97)( 26, 98)
( 27,103)( 28,104)( 29,105)( 30,106)( 31, 99)( 32,100)( 33,101)( 34,102)
( 35,107)( 36,108)( 37,109)( 38,110)( 39,115)( 40,116)( 41,117)( 42,118)
( 43,111)( 44,112)( 45,113)( 46,114)( 47,119)( 48,120)( 49,121)( 50,122)
( 51,127)( 52,128)( 53,129)( 54,130)( 55,123)( 56,124)( 57,125)( 58,126)
( 59,131)( 60,132)( 61,133)( 62,134)( 63,139)( 64,140)( 65,141)( 66,142)
( 67,135)( 68,136)( 69,137)( 70,138)( 71,143)( 72,144)( 73,145)( 74,146);;
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*s1*s2*s3*s1*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*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,  5)(  4,  6)(  7,  9)(  8, 10)( 11, 13)( 12, 14)( 15, 17)
( 16, 18)( 19, 21)( 20, 22)( 23, 25)( 24, 26)( 27, 29)( 28, 30)( 31, 33)
( 32, 34)( 35, 37)( 36, 38)( 39, 41)( 40, 42)( 43, 45)( 44, 46)( 47, 49)
( 48, 50)( 51, 53)( 52, 54)( 55, 57)( 56, 58)( 59, 61)( 60, 62)( 63, 65)
( 64, 66)( 67, 69)( 68, 70)( 71, 73)( 72, 74)( 75, 77)( 76, 78)( 79, 81)
( 80, 82)( 83, 85)( 84, 86)( 87, 89)( 88, 90)( 91, 93)( 92, 94)( 95, 97)
( 96, 98)( 99,101)(100,102)(103,105)(104,106)(107,109)(108,110)(111,113)
(112,114)(115,117)(116,118)(119,121)(120,122)(123,125)(124,126)(127,129)
(128,130)(131,133)(132,134)(135,137)(136,138)(139,141)(140,142)(143,145)
(144,146);
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)( 75,135)( 76,138)( 77,137)( 78,136)( 79,143)
( 80,146)( 81,145)( 82,144)( 83,139)( 84,142)( 85,141)( 86,140)( 87,123)
( 88,126)( 89,125)( 90,124)( 91,131)( 92,134)( 93,133)( 94,132)( 95,127)
( 96,130)( 97,129)( 98,128)( 99,111)(100,114)(101,113)(102,112)(103,119)
(104,122)(105,121)(106,120)(107,115)(108,118)(109,117)(110,116);
s4 := Sym(146)!(  3, 79)(  4, 80)(  5, 81)(  6, 82)(  7, 75)(  8, 76)(  9, 77)
( 10, 78)( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 91)( 16, 92)( 17, 93)
( 18, 94)( 19, 87)( 20, 88)( 21, 89)( 22, 90)( 23, 95)( 24, 96)( 25, 97)
( 26, 98)( 27,103)( 28,104)( 29,105)( 30,106)( 31, 99)( 32,100)( 33,101)
( 34,102)( 35,107)( 36,108)( 37,109)( 38,110)( 39,115)( 40,116)( 41,117)
( 42,118)( 43,111)( 44,112)( 45,113)( 46,114)( 47,119)( 48,120)( 49,121)
( 50,122)( 51,127)( 52,128)( 53,129)( 54,130)( 55,123)( 56,124)( 57,125)
( 58,126)( 59,131)( 60,132)( 61,133)( 62,134)( 63,139)( 64,140)( 65,141)
( 66,142)( 67,135)( 68,136)( 69,137)( 70,138)( 71,143)( 72,144)( 73,145)
( 74,146);
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*s1*s2*s3*s1*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*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 

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