Polytope of Type {4,18,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,18,2}*1152b
if this polytope has a name.
Group : SmallGroup(1152,155402)
Rank : 4
Schlafli Type : {4,18,2}
Number of vertices, edges, etc : 16, 144, 72, 2
Order of s0s1s2s3 : 36
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
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 : {4,18,2}*576
3-fold quotients : {4,6,2}*384b
4-fold quotients : {4,18,2}*288a, {4,9,2}*288, {4,18,2}*288b, {4,18,2}*288c
6-fold quotients : {4,6,2}*192
8-fold quotients : {4,9,2}*144, {2,18,2}*144
12-fold quotients : {4,6,2}*96a, {4,3,2}*96, {4,6,2}*96b, {4,6,2}*96c
16-fold quotients : {2,9,2}*72
24-fold quotients : {4,3,2}*48, {2,6,2}*48
36-fold quotients : {4,2,2}*32
48-fold quotients : {2,3,2}*24
72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)( 14, 16)
( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)
( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)
( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)
( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 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 := ( 1, 73)( 2, 75)( 3, 74)( 4, 76)( 5, 81)( 6, 83)( 7, 82)( 8, 84)
( 9, 77)( 10, 79)( 11, 78)( 12, 80)( 13,105)( 14,107)( 15,106)( 16,108)
( 17,101)( 18,103)( 19,102)( 20,104)( 21, 97)( 22, 99)( 23, 98)( 24,100)
( 25, 93)( 26, 95)( 27, 94)( 28, 96)( 29, 89)( 30, 91)( 31, 90)( 32, 92)
( 33, 85)( 34, 87)( 35, 86)( 36, 88)( 37,109)( 38,111)( 39,110)( 40,112)
( 41,117)( 42,119)( 43,118)( 44,120)( 45,113)( 46,115)( 47,114)( 48,116)
( 49,141)( 50,143)( 51,142)( 52,144)( 53,137)( 54,139)( 55,138)( 56,140)
( 57,133)( 58,135)( 59,134)( 60,136)( 61,129)( 62,131)( 63,130)( 64,132)
( 65,125)( 66,127)( 67,126)( 68,128)( 69,121)( 70,123)( 71,122)( 72,124);;
s2 := ( 1, 25)( 2, 28)( 3, 27)( 4, 26)( 5, 33)( 6, 36)( 7, 35)( 8, 34)
( 9, 29)( 10, 32)( 11, 31)( 12, 30)( 14, 16)( 17, 21)( 18, 24)( 19, 23)
( 20, 22)( 37, 61)( 38, 64)( 39, 63)( 40, 62)( 41, 69)( 42, 72)( 43, 71)
( 44, 70)( 45, 65)( 46, 68)( 47, 67)( 48, 66)( 50, 52)( 53, 57)( 54, 60)
( 55, 59)( 56, 58)( 73, 97)( 74,100)( 75, 99)( 76, 98)( 77,105)( 78,108)
( 79,107)( 80,106)( 81,101)( 82,104)( 83,103)( 84,102)( 86, 88)( 89, 93)
( 90, 96)( 91, 95)( 92, 94)(109,133)(110,136)(111,135)(112,134)(113,141)
(114,144)(115,143)(116,142)(117,137)(118,140)(119,139)(120,138)(122,124)
(125,129)(126,132)(127,131)(128,130);;
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,
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(146)!( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)
( 14, 16)( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)
( 30, 32)( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)
( 46, 48)( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)
( 62, 64)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 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)!( 1, 73)( 2, 75)( 3, 74)( 4, 76)( 5, 81)( 6, 83)( 7, 82)
( 8, 84)( 9, 77)( 10, 79)( 11, 78)( 12, 80)( 13,105)( 14,107)( 15,106)
( 16,108)( 17,101)( 18,103)( 19,102)( 20,104)( 21, 97)( 22, 99)( 23, 98)
( 24,100)( 25, 93)( 26, 95)( 27, 94)( 28, 96)( 29, 89)( 30, 91)( 31, 90)
( 32, 92)( 33, 85)( 34, 87)( 35, 86)( 36, 88)( 37,109)( 38,111)( 39,110)
( 40,112)( 41,117)( 42,119)( 43,118)( 44,120)( 45,113)( 46,115)( 47,114)
( 48,116)( 49,141)( 50,143)( 51,142)( 52,144)( 53,137)( 54,139)( 55,138)
( 56,140)( 57,133)( 58,135)( 59,134)( 60,136)( 61,129)( 62,131)( 63,130)
( 64,132)( 65,125)( 66,127)( 67,126)( 68,128)( 69,121)( 70,123)( 71,122)
( 72,124);
s2 := Sym(146)!( 1, 25)( 2, 28)( 3, 27)( 4, 26)( 5, 33)( 6, 36)( 7, 35)
( 8, 34)( 9, 29)( 10, 32)( 11, 31)( 12, 30)( 14, 16)( 17, 21)( 18, 24)
( 19, 23)( 20, 22)( 37, 61)( 38, 64)( 39, 63)( 40, 62)( 41, 69)( 42, 72)
( 43, 71)( 44, 70)( 45, 65)( 46, 68)( 47, 67)( 48, 66)( 50, 52)( 53, 57)
( 54, 60)( 55, 59)( 56, 58)( 73, 97)( 74,100)( 75, 99)( 76, 98)( 77,105)
( 78,108)( 79,107)( 80,106)( 81,101)( 82,104)( 83,103)( 84,102)( 86, 88)
( 89, 93)( 90, 96)( 91, 95)( 92, 94)(109,133)(110,136)(111,135)(112,134)
(113,141)(114,144)(115,143)(116,142)(117,137)(118,140)(119,139)(120,138)
(122,124)(125,129)(126,132)(127,131)(128,130);
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, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope