Polytope of Type {2,9,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,9,8}*1152
if this polytope has a name.
Group : SmallGroup(1152,154283)
Rank : 4
Schlafli Type : {2,9,8}
Number of vertices, edges, etc : 2, 36, 144, 32
Order of s₀s₁s₂s₃ : 18
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) :
   3-fold quotients : {2,3,8}*384
   4-fold quotients : {2,9,4}*288
   8-fold quotients : {2,9,4}*144
   12-fold quotients : {2,3,4}*96
   16-fold quotients : {2,9,2}*72
   24-fold quotients : {2,3,4}*48
   48-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

to this polytope