Polytope of Type {2,9,4,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,9,4,4}*1152a
if this polytope has a name.
Group : SmallGroup(1152,154282)
Rank : 5
Schlafli Type : {2,9,4,4}
Number of vertices, edges, etc : 2, 9, 36, 16, 8
Order of s₀s₁s₂s₃s₄ : 18
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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 : {2,3,4,4}*384a
   4-fold quotients : {2,9,4,2}*288
   12-fold quotients : {2,3,4,2}*96
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, 55)(  8, 58)(  9, 57)( 10, 56)
( 11, 63)( 12, 66)( 13, 65)( 14, 64)( 15, 59)( 16, 62)( 17, 61)( 18, 60)
( 19, 83)( 20, 86)( 21, 85)( 22, 84)( 23, 87)( 24, 90)( 25, 89)( 26, 88)
( 27, 95)( 28, 98)( 29, 97)( 30, 96)( 31, 91)( 32, 94)( 33, 93)( 34, 92)
( 35, 67)( 36, 70)( 37, 69)( 38, 68)( 39, 71)( 40, 74)( 41, 73)( 42, 72)
( 43, 79)( 44, 82)( 45, 81)( 46, 80)( 47, 75)( 48, 78)( 49, 77)( 50, 76)
( 99,115)(100,118)(101,117)(102,116)(103,119)(104,122)(105,121)(106,120)
(107,127)(108,130)(109,129)(110,128)(111,123)(112,126)(113,125)(114,124)
(132,134)(136,138)(139,143)(140,146)(141,145)(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);;
s4 := (  7,  9)(  8, 10)( 11, 14)( 12, 13)( 15, 16)( 17, 18)( 23, 25)( 24, 26)
( 27, 30)( 28, 29)( 31, 32)( 33, 34)( 39, 41)( 40, 42)( 43, 46)( 44, 45)
( 47, 48)( 49, 50)( 55, 57)( 56, 58)( 59, 62)( 60, 61)( 63, 64)( 65, 66)
( 71, 73)( 72, 74)( 75, 78)( 76, 77)( 79, 80)( 81, 82)( 87, 89)( 88, 90)
( 91, 94)( 92, 93)( 95, 96)( 97, 98)(103,105)(104,106)(107,110)(108,109)
(111,112)(113,114)(119,121)(120,122)(123,126)(124,125)(127,128)(129,130)
(135,137)(136,138)(139,142)(140,141)(143,144)(145,146);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s2*s1*s3*s2*s3*s2*s1*s2, s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3, 
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, 55)(  8, 58)(  9, 57)
( 10, 56)( 11, 63)( 12, 66)( 13, 65)( 14, 64)( 15, 59)( 16, 62)( 17, 61)
( 18, 60)( 19, 83)( 20, 86)( 21, 85)( 22, 84)( 23, 87)( 24, 90)( 25, 89)
( 26, 88)( 27, 95)( 28, 98)( 29, 97)( 30, 96)( 31, 91)( 32, 94)( 33, 93)
( 34, 92)( 35, 67)( 36, 70)( 37, 69)( 38, 68)( 39, 71)( 40, 74)( 41, 73)
( 42, 72)( 43, 79)( 44, 82)( 45, 81)( 46, 80)( 47, 75)( 48, 78)( 49, 77)
( 50, 76)( 99,115)(100,118)(101,117)(102,116)(103,119)(104,122)(105,121)
(106,120)(107,127)(108,130)(109,129)(110,128)(111,123)(112,126)(113,125)
(114,124)(132,134)(136,138)(139,143)(140,146)(141,145)(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);
s4 := Sym(146)!(  7,  9)(  8, 10)( 11, 14)( 12, 13)( 15, 16)( 17, 18)( 23, 25)
( 24, 26)( 27, 30)( 28, 29)( 31, 32)( 33, 34)( 39, 41)( 40, 42)( 43, 46)
( 44, 45)( 47, 48)( 49, 50)( 55, 57)( 56, 58)( 59, 62)( 60, 61)( 63, 64)
( 65, 66)( 71, 73)( 72, 74)( 75, 78)( 76, 77)( 79, 80)( 81, 82)( 87, 89)
( 88, 90)( 91, 94)( 92, 93)( 95, 96)( 97, 98)(103,105)(104,106)(107,110)
(108,109)(111,112)(113,114)(119,121)(120,122)(123,126)(124,125)(127,128)
(129,130)(135,137)(136,138)(139,142)(140,141)(143,144)(145,146);
poly := sub<Sym(146)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, s3*s2*s1*s3*s2*s3*s2*s1*s2, 
s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope