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}*1152e
if this polytope has a name.
Group : SmallGroup(1152,157640)
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}*576e
3-fold quotients : {2,4,6,4}*384c
4-fold quotients : {2,4,3,6}*288
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)( 7, 11)( 8, 13)( 9, 12)( 10, 14)( 15, 27)( 16, 29)( 17, 28)
( 18, 30)( 19, 35)( 20, 37)( 21, 36)( 22, 38)( 23, 31)( 24, 33)( 25, 32)
( 26, 34)( 40, 41)( 43, 47)( 44, 49)( 45, 48)( 46, 50)( 51, 63)( 52, 65)
( 53, 64)( 54, 66)( 55, 71)( 56, 73)( 57, 72)( 58, 74)( 59, 67)( 60, 69)
( 61, 68)( 62, 70)( 76, 77)( 79, 83)( 80, 85)( 81, 84)( 82, 86)( 87, 99)
( 88,101)( 89,100)( 90,102)( 91,107)( 92,109)( 93,108)( 94,110)( 95,103)
( 96,105)( 97,104)( 98,106)(112,113)(115,119)(116,121)(117,120)(118,122)
(123,135)(124,137)(125,136)(126,138)(127,143)(128,145)(129,144)(130,146)
(131,139)(132,141)(133,140)(134,142);;
s3 := ( 3,103)( 4,106)( 5,105)( 6,104)( 7, 99)( 8,102)( 9,101)( 10,100)
( 11,107)( 12,110)( 13,109)( 14,108)( 15, 91)( 16, 94)( 17, 93)( 18, 92)
( 19, 87)( 20, 90)( 21, 89)( 22, 88)( 23, 95)( 24, 98)( 25, 97)( 26, 96)
( 27, 79)( 28, 82)( 29, 81)( 30, 80)( 31, 75)( 32, 78)( 33, 77)( 34, 76)
( 35, 83)( 36, 86)( 37, 85)( 38, 84)( 39,139)( 40,142)( 41,141)( 42,140)
( 43,135)( 44,138)( 45,137)( 46,136)( 47,143)( 48,146)( 49,145)( 50,144)
( 51,127)( 52,130)( 53,129)( 54,128)( 55,123)( 56,126)( 57,125)( 58,124)
( 59,131)( 60,134)( 61,133)( 62,132)( 63,115)( 64,118)( 65,117)( 66,116)
( 67,111)( 68,114)( 69,113)( 70,112)( 71,119)( 72,122)( 73,121)( 74,120);;
s4 := ( 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)
( 75,111)( 76,112)( 77,113)( 78,114)( 79,119)( 80,120)( 81,121)( 82,122)
( 83,115)( 84,116)( 85,117)( 86,118)( 87,123)( 88,124)( 89,125)( 90,126)
( 91,131)( 92,132)( 93,133)( 94,134)( 95,127)( 96,128)( 97,129)( 98,130)
( 99,135)(100,136)(101,137)(102,138)(103,143)(104,144)(105,145)(106,146)
(107,139)(108,140)(109,141)(110,142);;
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, s1*s2*s3*s2*s1*s2*s3*s1*s2,
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
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)( 7, 11)( 8, 13)( 9, 12)( 10, 14)( 15, 27)( 16, 29)
( 17, 28)( 18, 30)( 19, 35)( 20, 37)( 21, 36)( 22, 38)( 23, 31)( 24, 33)
( 25, 32)( 26, 34)( 40, 41)( 43, 47)( 44, 49)( 45, 48)( 46, 50)( 51, 63)
( 52, 65)( 53, 64)( 54, 66)( 55, 71)( 56, 73)( 57, 72)( 58, 74)( 59, 67)
( 60, 69)( 61, 68)( 62, 70)( 76, 77)( 79, 83)( 80, 85)( 81, 84)( 82, 86)
( 87, 99)( 88,101)( 89,100)( 90,102)( 91,107)( 92,109)( 93,108)( 94,110)
( 95,103)( 96,105)( 97,104)( 98,106)(112,113)(115,119)(116,121)(117,120)
(118,122)(123,135)(124,137)(125,136)(126,138)(127,143)(128,145)(129,144)
(130,146)(131,139)(132,141)(133,140)(134,142);
s3 := Sym(146)!( 3,103)( 4,106)( 5,105)( 6,104)( 7, 99)( 8,102)( 9,101)
( 10,100)( 11,107)( 12,110)( 13,109)( 14,108)( 15, 91)( 16, 94)( 17, 93)
( 18, 92)( 19, 87)( 20, 90)( 21, 89)( 22, 88)( 23, 95)( 24, 98)( 25, 97)
( 26, 96)( 27, 79)( 28, 82)( 29, 81)( 30, 80)( 31, 75)( 32, 78)( 33, 77)
( 34, 76)( 35, 83)( 36, 86)( 37, 85)( 38, 84)( 39,139)( 40,142)( 41,141)
( 42,140)( 43,135)( 44,138)( 45,137)( 46,136)( 47,143)( 48,146)( 49,145)
( 50,144)( 51,127)( 52,130)( 53,129)( 54,128)( 55,123)( 56,126)( 57,125)
( 58,124)( 59,131)( 60,134)( 61,133)( 62,132)( 63,115)( 64,118)( 65,117)
( 66,116)( 67,111)( 68,114)( 69,113)( 70,112)( 71,119)( 72,122)( 73,121)
( 74,120);
s4 := 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)( 75,111)( 76,112)( 77,113)( 78,114)( 79,119)( 80,120)( 81,121)
( 82,122)( 83,115)( 84,116)( 85,117)( 86,118)( 87,123)( 88,124)( 89,125)
( 90,126)( 91,131)( 92,132)( 93,133)( 94,134)( 95,127)( 96,128)( 97,129)
( 98,130)( 99,135)(100,136)(101,137)(102,138)(103,143)(104,144)(105,145)
(106,146)(107,139)(108,140)(109,141)(110,142);
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,
s1*s2*s3*s2*s1*s2*s3*s1*s2, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope