Polytope of Type {4,12,6,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12,6,2}*1152g
if this polytope has a name.
Group : SmallGroup(1152,157549)
Rank : 5
Schlafli Type : {4,12,6,2}
Number of vertices, edges, etc : 4, 24, 36, 6, 2
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 : {4,6,6,2}*576e
3-fold quotients : {4,12,2,2}*384c
4-fold quotients : {4,3,6,2}*288
6-fold quotients : {4,6,2,2}*192c
12-fold quotients : {4,3,2,2}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 39)( 2, 40)( 3, 37)( 4, 38)( 5, 43)( 6, 44)( 7, 41)( 8, 42)
( 9, 47)( 10, 48)( 11, 45)( 12, 46)( 13, 51)( 14, 52)( 15, 49)( 16, 50)
( 17, 55)( 18, 56)( 19, 53)( 20, 54)( 21, 59)( 22, 60)( 23, 57)( 24, 58)
( 25, 63)( 26, 64)( 27, 61)( 28, 62)( 29, 67)( 30, 68)( 31, 65)( 32, 66)
( 33, 71)( 34, 72)( 35, 69)( 36, 70)( 73,111)( 74,112)( 75,109)( 76,110)
( 77,115)( 78,116)( 79,113)( 80,114)( 81,119)( 82,120)( 83,117)( 84,118)
( 85,123)( 86,124)( 87,121)( 88,122)( 89,127)( 90,128)( 91,125)( 92,126)
( 93,131)( 94,132)( 95,129)( 96,130)( 97,135)( 98,136)( 99,133)(100,134)
(101,139)(102,140)(103,137)(104,138)(105,143)(106,144)(107,141)(108,142);;
s1 := ( 2, 3)( 5, 9)( 6, 11)( 7, 10)( 8, 12)( 13, 25)( 14, 27)( 15, 26)
( 16, 28)( 17, 33)( 18, 35)( 19, 34)( 20, 36)( 21, 29)( 22, 31)( 23, 30)
( 24, 32)( 38, 39)( 41, 45)( 42, 47)( 43, 46)( 44, 48)( 49, 61)( 50, 63)
( 51, 62)( 52, 64)( 53, 69)( 54, 71)( 55, 70)( 56, 72)( 57, 65)( 58, 67)
( 59, 66)( 60, 68)( 73,109)( 74,111)( 75,110)( 76,112)( 77,117)( 78,119)
( 79,118)( 80,120)( 81,113)( 82,115)( 83,114)( 84,116)( 85,133)( 86,135)
( 87,134)( 88,136)( 89,141)( 90,143)( 91,142)( 92,144)( 93,137)( 94,139)
( 95,138)( 96,140)( 97,121)( 98,123)( 99,122)(100,124)(101,129)(102,131)
(103,130)(104,132)(105,125)(106,127)(107,126)(108,128);;
s2 := ( 1,101)( 2,104)( 3,103)( 4,102)( 5, 97)( 6,100)( 7, 99)( 8, 98)
( 9,105)( 10,108)( 11,107)( 12,106)( 13, 89)( 14, 92)( 15, 91)( 16, 90)
( 17, 85)( 18, 88)( 19, 87)( 20, 86)( 21, 93)( 22, 96)( 23, 95)( 24, 94)
( 25, 77)( 26, 80)( 27, 79)( 28, 78)( 29, 73)( 30, 76)( 31, 75)( 32, 74)
( 33, 81)( 34, 84)( 35, 83)( 36, 82)( 37,137)( 38,140)( 39,139)( 40,138)
( 41,133)( 42,136)( 43,135)( 44,134)( 45,141)( 46,144)( 47,143)( 48,142)
( 49,125)( 50,128)( 51,127)( 52,126)( 53,121)( 54,124)( 55,123)( 56,122)
( 57,129)( 58,132)( 59,131)( 60,130)( 61,113)( 62,116)( 63,115)( 64,114)
( 65,109)( 66,112)( 67,111)( 68,110)( 69,117)( 70,120)( 71,119)( 72,118);;
s3 := ( 5, 9)( 6, 10)( 7, 11)( 8, 12)( 17, 21)( 18, 22)( 19, 23)( 20, 24)
( 29, 33)( 30, 34)( 31, 35)( 32, 36)( 41, 45)( 42, 46)( 43, 47)( 44, 48)
( 53, 57)( 54, 58)( 55, 59)( 56, 60)( 65, 69)( 66, 70)( 67, 71)( 68, 72)
( 77, 81)( 78, 82)( 79, 83)( 80, 84)( 89, 93)( 90, 94)( 91, 95)( 92, 96)
(101,105)(102,106)(103,107)(104,108)(113,117)(114,118)(115,119)(116,120)
(125,129)(126,130)(127,131)(128,132)(137,141)(138,142)(139,143)(140,144);;
s4 := (145,146);;
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*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,
s0*s1*s0*s1*s0*s1*s0*s1, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(146)!( 1, 39)( 2, 40)( 3, 37)( 4, 38)( 5, 43)( 6, 44)( 7, 41)
( 8, 42)( 9, 47)( 10, 48)( 11, 45)( 12, 46)( 13, 51)( 14, 52)( 15, 49)
( 16, 50)( 17, 55)( 18, 56)( 19, 53)( 20, 54)( 21, 59)( 22, 60)( 23, 57)
( 24, 58)( 25, 63)( 26, 64)( 27, 61)( 28, 62)( 29, 67)( 30, 68)( 31, 65)
( 32, 66)( 33, 71)( 34, 72)( 35, 69)( 36, 70)( 73,111)( 74,112)( 75,109)
( 76,110)( 77,115)( 78,116)( 79,113)( 80,114)( 81,119)( 82,120)( 83,117)
( 84,118)( 85,123)( 86,124)( 87,121)( 88,122)( 89,127)( 90,128)( 91,125)
( 92,126)( 93,131)( 94,132)( 95,129)( 96,130)( 97,135)( 98,136)( 99,133)
(100,134)(101,139)(102,140)(103,137)(104,138)(105,143)(106,144)(107,141)
(108,142);
s1 := Sym(146)!( 2, 3)( 5, 9)( 6, 11)( 7, 10)( 8, 12)( 13, 25)( 14, 27)
( 15, 26)( 16, 28)( 17, 33)( 18, 35)( 19, 34)( 20, 36)( 21, 29)( 22, 31)
( 23, 30)( 24, 32)( 38, 39)( 41, 45)( 42, 47)( 43, 46)( 44, 48)( 49, 61)
( 50, 63)( 51, 62)( 52, 64)( 53, 69)( 54, 71)( 55, 70)( 56, 72)( 57, 65)
( 58, 67)( 59, 66)( 60, 68)( 73,109)( 74,111)( 75,110)( 76,112)( 77,117)
( 78,119)( 79,118)( 80,120)( 81,113)( 82,115)( 83,114)( 84,116)( 85,133)
( 86,135)( 87,134)( 88,136)( 89,141)( 90,143)( 91,142)( 92,144)( 93,137)
( 94,139)( 95,138)( 96,140)( 97,121)( 98,123)( 99,122)(100,124)(101,129)
(102,131)(103,130)(104,132)(105,125)(106,127)(107,126)(108,128);
s2 := Sym(146)!( 1,101)( 2,104)( 3,103)( 4,102)( 5, 97)( 6,100)( 7, 99)
( 8, 98)( 9,105)( 10,108)( 11,107)( 12,106)( 13, 89)( 14, 92)( 15, 91)
( 16, 90)( 17, 85)( 18, 88)( 19, 87)( 20, 86)( 21, 93)( 22, 96)( 23, 95)
( 24, 94)( 25, 77)( 26, 80)( 27, 79)( 28, 78)( 29, 73)( 30, 76)( 31, 75)
( 32, 74)( 33, 81)( 34, 84)( 35, 83)( 36, 82)( 37,137)( 38,140)( 39,139)
( 40,138)( 41,133)( 42,136)( 43,135)( 44,134)( 45,141)( 46,144)( 47,143)
( 48,142)( 49,125)( 50,128)( 51,127)( 52,126)( 53,121)( 54,124)( 55,123)
( 56,122)( 57,129)( 58,132)( 59,131)( 60,130)( 61,113)( 62,116)( 63,115)
( 64,114)( 65,109)( 66,112)( 67,111)( 68,110)( 69,117)( 70,120)( 71,119)
( 72,118);
s3 := Sym(146)!( 5, 9)( 6, 10)( 7, 11)( 8, 12)( 17, 21)( 18, 22)( 19, 23)
( 20, 24)( 29, 33)( 30, 34)( 31, 35)( 32, 36)( 41, 45)( 42, 46)( 43, 47)
( 44, 48)( 53, 57)( 54, 58)( 55, 59)( 56, 60)( 65, 69)( 66, 70)( 67, 71)
( 68, 72)( 77, 81)( 78, 82)( 79, 83)( 80, 84)( 89, 93)( 90, 94)( 91, 95)
( 92, 96)(101,105)(102,106)(103,107)(104,108)(113,117)(114,118)(115,119)
(116,120)(125,129)(126,130)(127,131)(128,132)(137,141)(138,142)(139,143)
(140,144);
s4 := Sym(146)!(145,146);
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*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, s0*s1*s0*s1*s0*s1*s0*s1,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1 >;
to this polytope