Polytope of Type {4,18}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,18}*576a
if this polytope has a name.
Group : SmallGroup(576,1380)
Rank : 3
Schlafli Type : {4,18}
Number of vertices, edges, etc : 16, 144, 72
Order of s₀s₁s₂ : 18
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,18,2} of size 1152
Vertex Figure Of :
   {2,4,18} of size 1152
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {4,6}*192a
   4-fold quotients : {4,18}*144b
   8-fold quotients : {4,9}*72
   12-fold quotients : {4,6}*48c
   24-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,36}*1152b, {4,36}*1152c, {8,18}*1152b, {8,18}*1152c, {4,18}*1152a
   3-fold covers : {4,54}*1728a
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, 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*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s0*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 >;

References : None.
to this polytope