Polytope of Type {18,4,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {18,4,2}*1152a
if this polytope has a name.
Group : SmallGroup(1152,154282)
Rank : 4
Schlafli Type : {18,4,2}
Number of vertices, edges, etc : 72, 144, 16, 2
Order of s0s1s2s3 : 18
Order of s0s1s2s3s2s1 : 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) :
3-fold quotients : {6,4,2}*384a
4-fold quotients : {18,4,2}*288b
8-fold quotients : {9,4,2}*144
12-fold quotients : {6,4,2}*96c
24-fold quotients : {3,4,2}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 15, 16)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 41)( 22, 42)( 23, 44)( 24, 43)( 25, 37)( 26, 38)( 27, 40)( 28, 39)( 29, 45)( 30, 46)( 31, 48)( 32, 47)( 49,113)( 50,114)( 51,116)( 52,115)( 53,121)( 54,122)( 55,124)( 56,123)( 57,117)( 58,118)( 59,120)( 60,119)( 61,125)( 62,126)( 63,128)( 64,127)( 65, 97)( 66, 98)( 67,100)( 68, 99)( 69,105)( 70,106)( 71,108)( 72,107)( 73,101)( 74,102)( 75,104)( 76,103)( 77,109)( 78,110)( 79,112)( 80,111)( 81,129)( 82,130)( 83,132)( 84,131)( 85,137)( 86,138)( 87,140)( 88,139)( 89,133)( 90,134)( 91,136)( 92,135)( 93,141)( 94,142)( 95,144)( 96,143);;
s1 := ( 1, 49)( 2, 52)( 3, 51)( 4, 50)( 5, 55)( 6, 54)( 7, 53)( 8, 56)( 9, 62)( 10, 63)( 11, 64)( 12, 61)( 13, 60)( 14, 57)( 15, 58)( 16, 59)( 17, 81)( 18, 84)( 19, 83)( 20, 82)( 21, 87)( 22, 86)( 23, 85)( 24, 88)( 25, 94)( 26, 95)( 27, 96)( 28, 93)( 29, 92)( 30, 89)( 31, 90)( 32, 91)( 33, 65)( 34, 68)( 35, 67)( 36, 66)( 37, 71)( 38, 70)( 39, 69)( 40, 72)( 41, 78)( 42, 79)( 43, 80)( 44, 77)( 45, 76)( 46, 73)( 47, 74)( 48, 75)( 97,113)( 98,116)( 99,115)(100,114)(101,119)(102,118)(103,117)(104,120)(105,126)(106,127)(107,128)(108,125)(109,124)(110,121)(111,122)(112,123)(130,132)(133,135)(137,142)(138,143)(139,144)(140,141);;
s2 := ( 1, 13)( 2, 14)( 3, 15)( 4, 16)( 5, 9)( 6, 10)( 7, 11)( 8, 12)( 17, 29)( 18, 30)( 19, 31)( 20, 32)( 21, 25)( 22, 26)( 23, 27)( 24, 28)( 33, 45)( 34, 46)( 35, 47)( 36, 48)( 37, 41)( 38, 42)( 39, 43)( 40, 44)( 49, 61)( 50, 62)( 51, 63)( 52, 64)( 53, 57)( 54, 58)( 55, 59)( 56, 60)( 65, 77)( 66, 78)( 67, 79)( 68, 80)( 69, 73)( 70, 74)( 71, 75)( 72, 76)( 81, 93)( 82, 94)( 83, 95)( 84, 96)( 85, 89)( 86, 90)( 87, 91)( 88, 92)( 97,109)( 98,110)( 99,111)(100,112)(101,105)(102,106)(103,107)(104,108)(113,125)(114,126)(115,127)(116,128)(117,121)(118,122)(119,123)(120,124)(129,141)(130,142)(131,143)(132,144)(133,137)(134,138)(135,139)(136,140);;
s3 := (145,146);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(146)!( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 15, 16)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 41)( 22, 42)( 23, 44)( 24, 43)( 25, 37)( 26, 38)( 27, 40)( 28, 39)( 29, 45)( 30, 46)( 31, 48)( 32, 47)( 49,113)( 50,114)( 51,116)( 52,115)( 53,121)( 54,122)( 55,124)( 56,123)( 57,117)( 58,118)( 59,120)( 60,119)( 61,125)( 62,126)( 63,128)( 64,127)( 65, 97)( 66, 98)( 67,100)( 68, 99)( 69,105)( 70,106)( 71,108)( 72,107)( 73,101)( 74,102)( 75,104)( 76,103)( 77,109)( 78,110)( 79,112)( 80,111)( 81,129)( 82,130)( 83,132)( 84,131)( 85,137)( 86,138)( 87,140)( 88,139)( 89,133)( 90,134)( 91,136)( 92,135)( 93,141)( 94,142)( 95,144)( 96,143);
s1 := Sym(146)!( 1, 49)( 2, 52)( 3, 51)( 4, 50)( 5, 55)( 6, 54)( 7, 53)( 8, 56)( 9, 62)( 10, 63)( 11, 64)( 12, 61)( 13, 60)( 14, 57)( 15, 58)( 16, 59)( 17, 81)( 18, 84)( 19, 83)( 20, 82)( 21, 87)( 22, 86)( 23, 85)( 24, 88)( 25, 94)( 26, 95)( 27, 96)( 28, 93)( 29, 92)( 30, 89)( 31, 90)( 32, 91)( 33, 65)( 34, 68)( 35, 67)( 36, 66)( 37, 71)( 38, 70)( 39, 69)( 40, 72)( 41, 78)( 42, 79)( 43, 80)( 44, 77)( 45, 76)( 46, 73)( 47, 74)( 48, 75)( 97,113)( 98,116)( 99,115)(100,114)(101,119)(102,118)(103,117)(104,120)(105,126)(106,127)(107,128)(108,125)(109,124)(110,121)(111,122)(112,123)(130,132)(133,135)(137,142)(138,143)(139,144)(140,141);
s2 := Sym(146)!( 1, 13)( 2, 14)( 3, 15)( 4, 16)( 5, 9)( 6, 10)( 7, 11)( 8, 12)( 17, 29)( 18, 30)( 19, 31)( 20, 32)( 21, 25)( 22, 26)( 23, 27)( 24, 28)( 33, 45)( 34, 46)( 35, 47)( 36, 48)( 37, 41)( 38, 42)( 39, 43)( 40, 44)( 49, 61)( 50, 62)( 51, 63)( 52, 64)( 53, 57)( 54, 58)( 55, 59)( 56, 60)( 65, 77)( 66, 78)( 67, 79)( 68, 80)( 69, 73)( 70, 74)( 71, 75)( 72, 76)( 81, 93)( 82, 94)( 83, 95)( 84, 96)( 85, 89)( 86, 90)( 87, 91)( 88, 92)( 97,109)( 98,110)( 99,111)(100,112)(101,105)(102,106)(103,107)(104,108)(113,125)(114,126)(115,127)(116,128)(117,121)(118,122)(119,123)(120,124)(129,141)(130,142)(131,143)(132,144)(133,137)(134,138)(135,139)(136,140);
s3 := Sym(146)!(145,146);
poly := sub<Sym(146)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
to this polytope