Polytope of Type {2,18,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,18,4}*1152a
if this polytope has a name.
Group : SmallGroup(1152,154282)
Rank : 4
Schlafli Type : {2,18,4}
Number of vertices, edges, etc : 2, 72, 144, 16
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 : {2,6,4}*384a
   4-fold quotients : {2,18,4}*288b
   8-fold quotients : {2,9,4}*144
   12-fold quotients : {2,6,4}*96c
   24-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  5,  6)(  7, 11)(  8, 12)(  9, 14)( 10, 13)( 17, 18)( 19, 35)( 20, 36)
( 21, 38)( 22, 37)( 23, 43)( 24, 44)( 25, 46)( 26, 45)( 27, 39)( 28, 40)
( 29, 42)( 30, 41)( 31, 47)( 32, 48)( 33, 50)( 34, 49)( 51,115)( 52,116)
( 53,118)( 54,117)( 55,123)( 56,124)( 57,126)( 58,125)( 59,119)( 60,120)
( 61,122)( 62,121)( 63,127)( 64,128)( 65,130)( 66,129)( 67, 99)( 68,100)
( 69,102)( 70,101)( 71,107)( 72,108)( 73,110)( 74,109)( 75,103)( 76,104)
( 77,106)( 78,105)( 79,111)( 80,112)( 81,114)( 82,113)( 83,131)( 84,132)
( 85,134)( 86,133)( 87,139)( 88,140)( 89,142)( 90,141)( 91,135)( 92,136)
( 93,138)( 94,137)( 95,143)( 96,144)( 97,146)( 98,145);;
s2 := (  3, 51)(  4, 54)(  5, 53)(  6, 52)(  7, 57)(  8, 56)(  9, 55)( 10, 58)
( 11, 64)( 12, 65)( 13, 66)( 14, 63)( 15, 62)( 16, 59)( 17, 60)( 18, 61)
( 19, 83)( 20, 86)( 21, 85)( 22, 84)( 23, 89)( 24, 88)( 25, 87)( 26, 90)
( 27, 96)( 28, 97)( 29, 98)( 30, 95)( 31, 94)( 32, 91)( 33, 92)( 34, 93)
( 35, 67)( 36, 70)( 37, 69)( 38, 68)( 39, 73)( 40, 72)( 41, 71)( 42, 74)
( 43, 80)( 44, 81)( 45, 82)( 46, 79)( 47, 78)( 48, 75)( 49, 76)( 50, 77)
( 99,115)(100,118)(101,117)(102,116)(103,121)(104,120)(105,119)(106,122)
(107,128)(108,129)(109,130)(110,127)(111,126)(112,123)(113,124)(114,125)
(132,134)(135,137)(139,144)(140,145)(141,146)(142,143);;
s3 := (  3, 15)(  4, 16)(  5, 17)(  6, 18)(  7, 11)(  8, 12)(  9, 13)( 10, 14)
( 19, 31)( 20, 32)( 21, 33)( 22, 34)( 23, 27)( 24, 28)( 25, 29)( 26, 30)
( 35, 47)( 36, 48)( 37, 49)( 38, 50)( 39, 43)( 40, 44)( 41, 45)( 42, 46)
( 51, 63)( 52, 64)( 53, 65)( 54, 66)( 55, 59)( 56, 60)( 57, 61)( 58, 62)
( 67, 79)( 68, 80)( 69, 81)( 70, 82)( 71, 75)( 72, 76)( 73, 77)( 74, 78)
( 83, 95)( 84, 96)( 85, 97)( 86, 98)( 87, 91)( 88, 92)( 89, 93)( 90, 94)
( 99,111)(100,112)(101,113)(102,114)(103,107)(104,108)(105,109)(106,110)
(115,127)(116,128)(117,129)(118,130)(119,123)(120,124)(121,125)(122,126)
(131,143)(132,144)(133,145)(134,146)(135,139)(136,140)(137,141)(138,142);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s3, 
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)!(1,2);
s1 := Sym(146)!(  5,  6)(  7, 11)(  8, 12)(  9, 14)( 10, 13)( 17, 18)( 19, 35)
( 20, 36)( 21, 38)( 22, 37)( 23, 43)( 24, 44)( 25, 46)( 26, 45)( 27, 39)
( 28, 40)( 29, 42)( 30, 41)( 31, 47)( 32, 48)( 33, 50)( 34, 49)( 51,115)
( 52,116)( 53,118)( 54,117)( 55,123)( 56,124)( 57,126)( 58,125)( 59,119)
( 60,120)( 61,122)( 62,121)( 63,127)( 64,128)( 65,130)( 66,129)( 67, 99)
( 68,100)( 69,102)( 70,101)( 71,107)( 72,108)( 73,110)( 74,109)( 75,103)
( 76,104)( 77,106)( 78,105)( 79,111)( 80,112)( 81,114)( 82,113)( 83,131)
( 84,132)( 85,134)( 86,133)( 87,139)( 88,140)( 89,142)( 90,141)( 91,135)
( 92,136)( 93,138)( 94,137)( 95,143)( 96,144)( 97,146)( 98,145);
s2 := Sym(146)!(  3, 51)(  4, 54)(  5, 53)(  6, 52)(  7, 57)(  8, 56)(  9, 55)
( 10, 58)( 11, 64)( 12, 65)( 13, 66)( 14, 63)( 15, 62)( 16, 59)( 17, 60)
( 18, 61)( 19, 83)( 20, 86)( 21, 85)( 22, 84)( 23, 89)( 24, 88)( 25, 87)
( 26, 90)( 27, 96)( 28, 97)( 29, 98)( 30, 95)( 31, 94)( 32, 91)( 33, 92)
( 34, 93)( 35, 67)( 36, 70)( 37, 69)( 38, 68)( 39, 73)( 40, 72)( 41, 71)
( 42, 74)( 43, 80)( 44, 81)( 45, 82)( 46, 79)( 47, 78)( 48, 75)( 49, 76)
( 50, 77)( 99,115)(100,118)(101,117)(102,116)(103,121)(104,120)(105,119)
(106,122)(107,128)(108,129)(109,130)(110,127)(111,126)(112,123)(113,124)
(114,125)(132,134)(135,137)(139,144)(140,145)(141,146)(142,143);
s3 := Sym(146)!(  3, 15)(  4, 16)(  5, 17)(  6, 18)(  7, 11)(  8, 12)(  9, 13)
( 10, 14)( 19, 31)( 20, 32)( 21, 33)( 22, 34)( 23, 27)( 24, 28)( 25, 29)
( 26, 30)( 35, 47)( 36, 48)( 37, 49)( 38, 50)( 39, 43)( 40, 44)( 41, 45)
( 42, 46)( 51, 63)( 52, 64)( 53, 65)( 54, 66)( 55, 59)( 56, 60)( 57, 61)
( 58, 62)( 67, 79)( 68, 80)( 69, 81)( 70, 82)( 71, 75)( 72, 76)( 73, 77)
( 74, 78)( 83, 95)( 84, 96)( 85, 97)( 86, 98)( 87, 91)( 88, 92)( 89, 93)
( 90, 94)( 99,111)(100,112)(101,113)(102,114)(103,107)(104,108)(105,109)
(106,110)(115,127)(116,128)(117,129)(118,130)(119,123)(120,124)(121,125)
(122,126)(131,143)(132,144)(133,145)(134,146)(135,139)(136,140)(137,141)
(138,142);
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, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s3, 
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