Polytope of Type {2,4,12,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,12,6}*1152d
if this polytope has a name.
Group : SmallGroup(1152,157549)
Rank : 5
Schlafli Type : {2,4,12,6}
Number of vertices, edges, etc : 2, 4, 24, 36, 6
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 : {2,4,12,2}*384b
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)( 75,111)( 76,113)
( 77,112)( 78,114)( 79,115)( 80,117)( 81,116)( 82,118)( 83,119)( 84,121)
( 85,120)( 86,122)( 87,135)( 88,137)( 89,136)( 90,138)( 91,139)( 92,141)
( 93,140)( 94,142)( 95,143)( 96,145)( 97,144)( 98,146)( 99,123)(100,125)
(101,124)(102,126)(103,127)(104,129)(105,128)(106,130)(107,131)(108,133)
(109,132)(110,134);;
s3 := ( 3, 99)( 4,102)( 5,101)( 6,100)( 7,107)( 8,110)( 9,109)( 10,108)
( 11,103)( 12,106)( 13,105)( 14,104)( 15, 87)( 16, 90)( 17, 89)( 18, 88)
( 19, 95)( 20, 98)( 21, 97)( 22, 96)( 23, 91)( 24, 94)( 25, 93)( 26, 92)
( 27, 75)( 28, 78)( 29, 77)( 30, 76)( 31, 83)( 32, 86)( 33, 85)( 34, 84)
( 35, 79)( 36, 82)( 37, 81)( 38, 80)( 39,135)( 40,138)( 41,137)( 42,136)
( 43,143)( 44,146)( 45,145)( 46,144)( 47,139)( 48,142)( 49,141)( 50,140)
( 51,123)( 52,126)( 53,125)( 54,124)( 55,131)( 56,134)( 57,133)( 58,132)
( 59,127)( 60,130)( 61,129)( 62,128)( 63,111)( 64,114)( 65,113)( 66,112)
( 67,119)( 68,122)( 69,121)( 70,120)( 71,115)( 72,118)( 73,117)( 74,116);;
s4 := ( 3, 7)( 4, 8)( 5, 9)( 6, 10)( 15, 19)( 16, 20)( 17, 21)( 18, 22)
( 27, 31)( 28, 32)( 29, 33)( 30, 34)( 39, 43)( 40, 44)( 41, 45)( 42, 46)
( 51, 55)( 52, 56)( 53, 57)( 54, 58)( 63, 67)( 64, 68)( 65, 69)( 66, 70)
( 75, 79)( 76, 80)( 77, 81)( 78, 82)( 87, 91)( 88, 92)( 89, 93)( 90, 94)
( 99,103)(100,104)(101,105)(102,106)(111,115)(112,116)(113,117)(114,118)
(123,127)(124,128)(125,129)(126,130)(135,139)(136,140)(137,141)(138,142);;
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, s2*s3*s4*s3*s2*s3*s4*s3,
s1*s2*s3*s2*s1*s2*s3*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*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)( 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)( 75,111)
( 76,113)( 77,112)( 78,114)( 79,115)( 80,117)( 81,116)( 82,118)( 83,119)
( 84,121)( 85,120)( 86,122)( 87,135)( 88,137)( 89,136)( 90,138)( 91,139)
( 92,141)( 93,140)( 94,142)( 95,143)( 96,145)( 97,144)( 98,146)( 99,123)
(100,125)(101,124)(102,126)(103,127)(104,129)(105,128)(106,130)(107,131)
(108,133)(109,132)(110,134);
s3 := Sym(146)!( 3, 99)( 4,102)( 5,101)( 6,100)( 7,107)( 8,110)( 9,109)
( 10,108)( 11,103)( 12,106)( 13,105)( 14,104)( 15, 87)( 16, 90)( 17, 89)
( 18, 88)( 19, 95)( 20, 98)( 21, 97)( 22, 96)( 23, 91)( 24, 94)( 25, 93)
( 26, 92)( 27, 75)( 28, 78)( 29, 77)( 30, 76)( 31, 83)( 32, 86)( 33, 85)
( 34, 84)( 35, 79)( 36, 82)( 37, 81)( 38, 80)( 39,135)( 40,138)( 41,137)
( 42,136)( 43,143)( 44,146)( 45,145)( 46,144)( 47,139)( 48,142)( 49,141)
( 50,140)( 51,123)( 52,126)( 53,125)( 54,124)( 55,131)( 56,134)( 57,133)
( 58,132)( 59,127)( 60,130)( 61,129)( 62,128)( 63,111)( 64,114)( 65,113)
( 66,112)( 67,119)( 68,122)( 69,121)( 70,120)( 71,115)( 72,118)( 73,117)
( 74,116);
s4 := Sym(146)!( 3, 7)( 4, 8)( 5, 9)( 6, 10)( 15, 19)( 16, 20)( 17, 21)
( 18, 22)( 27, 31)( 28, 32)( 29, 33)( 30, 34)( 39, 43)( 40, 44)( 41, 45)
( 42, 46)( 51, 55)( 52, 56)( 53, 57)( 54, 58)( 63, 67)( 64, 68)( 65, 69)
( 66, 70)( 75, 79)( 76, 80)( 77, 81)( 78, 82)( 87, 91)( 88, 92)( 89, 93)
( 90, 94)( 99,103)(100,104)(101,105)(102,106)(111,115)(112,116)(113,117)
(114,118)(123,127)(124,128)(125,129)(126,130)(135,139)(136,140)(137,141)
(138,142);
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,
s2*s3*s4*s3*s2*s3*s4*s3, s1*s2*s3*s2*s1*s2*s3*s1*s2,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope