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Polytope of Type {2,4,18}

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

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