Polytope of Type {2,111,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,111,4}*1776
if this polytope has a name.
Group : SmallGroup(1776,245)
Rank : 4
Schlafli Type : {2,111,4}
Number of vertices, edges, etc : 2, 111, 222, 4
Order of s₀s₁s₂s₃ : 222
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) :
   37-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4,  5)(  7,147)(  8,149)(  9,148)( 10,150)( 11,143)( 12,145)( 13,144)
( 14,146)( 15,139)( 16,141)( 17,140)( 18,142)( 19,135)( 20,137)( 21,136)
( 22,138)( 23,131)( 24,133)( 25,132)( 26,134)( 27,127)( 28,129)( 29,128)
( 30,130)( 31,123)( 32,125)( 33,124)( 34,126)( 35,119)( 36,121)( 37,120)
( 38,122)( 39,115)( 40,117)( 41,116)( 42,118)( 43,111)( 44,113)( 45,112)
( 46,114)( 47,107)( 48,109)( 49,108)( 50,110)( 51,103)( 52,105)( 53,104)
( 54,106)( 55, 99)( 56,101)( 57,100)( 58,102)( 59, 95)( 60, 97)( 61, 96)
( 62, 98)( 63, 91)( 64, 93)( 65, 92)( 66, 94)( 67, 87)( 68, 89)( 69, 88)
( 70, 90)( 71, 83)( 72, 85)( 73, 84)( 74, 86)( 75, 79)( 76, 81)( 77, 80)
( 78, 82);;
s2 := (  3,  7)(  4,  8)(  5, 10)(  6,  9)( 11,147)( 12,148)( 13,150)( 14,149)
( 15,143)( 16,144)( 17,146)( 18,145)( 19,139)( 20,140)( 21,142)( 22,141)
( 23,135)( 24,136)( 25,138)( 26,137)( 27,131)( 28,132)( 29,134)( 30,133)
( 31,127)( 32,128)( 33,130)( 34,129)( 35,123)( 36,124)( 37,126)( 38,125)
( 39,119)( 40,120)( 41,122)( 42,121)( 43,115)( 44,116)( 45,118)( 46,117)
( 47,111)( 48,112)( 49,114)( 50,113)( 51,107)( 52,108)( 53,110)( 54,109)
( 55,103)( 56,104)( 57,106)( 58,105)( 59, 99)( 60,100)( 61,102)( 62,101)
( 63, 95)( 64, 96)( 65, 98)( 66, 97)( 67, 91)( 68, 92)( 69, 94)( 70, 93)
( 71, 87)( 72, 88)( 73, 90)( 74, 89)( 75, 83)( 76, 84)( 77, 86)( 78, 85)
( 81, 82);;
s3 := (  3,  6)(  4,  5)(  7, 10)(  8,  9)( 11, 14)( 12, 13)( 15, 18)( 16, 17)
( 19, 22)( 20, 21)( 23, 26)( 24, 25)( 27, 30)( 28, 29)( 31, 34)( 32, 33)
( 35, 38)( 36, 37)( 39, 42)( 40, 41)( 43, 46)( 44, 45)( 47, 50)( 48, 49)
( 51, 54)( 52, 53)( 55, 58)( 56, 57)( 59, 62)( 60, 61)( 63, 66)( 64, 65)
( 67, 70)( 68, 69)( 71, 74)( 72, 73)( 75, 78)( 76, 77)( 79, 82)( 80, 81)
( 83, 86)( 84, 85)( 87, 90)( 88, 89)( 91, 94)( 92, 93)( 95, 98)( 96, 97)
( 99,102)(100,101)(103,106)(104,105)(107,110)(108,109)(111,114)(112,113)
(115,118)(116,117)(119,122)(120,121)(123,126)(124,125)(127,130)(128,129)
(131,134)(132,133)(135,138)(136,137)(139,142)(140,141)(143,146)(144,145)
(147,150)(148,149);;
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, s3*s2*s1*s3*s2*s3*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*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*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*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*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*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(150)!(1,2);
s1 := Sym(150)!(  4,  5)(  7,147)(  8,149)(  9,148)( 10,150)( 11,143)( 12,145)
( 13,144)( 14,146)( 15,139)( 16,141)( 17,140)( 18,142)( 19,135)( 20,137)
( 21,136)( 22,138)( 23,131)( 24,133)( 25,132)( 26,134)( 27,127)( 28,129)
( 29,128)( 30,130)( 31,123)( 32,125)( 33,124)( 34,126)( 35,119)( 36,121)
( 37,120)( 38,122)( 39,115)( 40,117)( 41,116)( 42,118)( 43,111)( 44,113)
( 45,112)( 46,114)( 47,107)( 48,109)( 49,108)( 50,110)( 51,103)( 52,105)
( 53,104)( 54,106)( 55, 99)( 56,101)( 57,100)( 58,102)( 59, 95)( 60, 97)
( 61, 96)( 62, 98)( 63, 91)( 64, 93)( 65, 92)( 66, 94)( 67, 87)( 68, 89)
( 69, 88)( 70, 90)( 71, 83)( 72, 85)( 73, 84)( 74, 86)( 75, 79)( 76, 81)
( 77, 80)( 78, 82);
s2 := Sym(150)!(  3,  7)(  4,  8)(  5, 10)(  6,  9)( 11,147)( 12,148)( 13,150)
( 14,149)( 15,143)( 16,144)( 17,146)( 18,145)( 19,139)( 20,140)( 21,142)
( 22,141)( 23,135)( 24,136)( 25,138)( 26,137)( 27,131)( 28,132)( 29,134)
( 30,133)( 31,127)( 32,128)( 33,130)( 34,129)( 35,123)( 36,124)( 37,126)
( 38,125)( 39,119)( 40,120)( 41,122)( 42,121)( 43,115)( 44,116)( 45,118)
( 46,117)( 47,111)( 48,112)( 49,114)( 50,113)( 51,107)( 52,108)( 53,110)
( 54,109)( 55,103)( 56,104)( 57,106)( 58,105)( 59, 99)( 60,100)( 61,102)
( 62,101)( 63, 95)( 64, 96)( 65, 98)( 66, 97)( 67, 91)( 68, 92)( 69, 94)
( 70, 93)( 71, 87)( 72, 88)( 73, 90)( 74, 89)( 75, 83)( 76, 84)( 77, 86)
( 78, 85)( 81, 82);
s3 := Sym(150)!(  3,  6)(  4,  5)(  7, 10)(  8,  9)( 11, 14)( 12, 13)( 15, 18)
( 16, 17)( 19, 22)( 20, 21)( 23, 26)( 24, 25)( 27, 30)( 28, 29)( 31, 34)
( 32, 33)( 35, 38)( 36, 37)( 39, 42)( 40, 41)( 43, 46)( 44, 45)( 47, 50)
( 48, 49)( 51, 54)( 52, 53)( 55, 58)( 56, 57)( 59, 62)( 60, 61)( 63, 66)
( 64, 65)( 67, 70)( 68, 69)( 71, 74)( 72, 73)( 75, 78)( 76, 77)( 79, 82)
( 80, 81)( 83, 86)( 84, 85)( 87, 90)( 88, 89)( 91, 94)( 92, 93)( 95, 98)
( 96, 97)( 99,102)(100,101)(103,106)(104,105)(107,110)(108,109)(111,114)
(112,113)(115,118)(116,117)(119,122)(120,121)(123,126)(124,125)(127,130)
(128,129)(131,134)(132,133)(135,138)(136,137)(139,142)(140,141)(143,146)
(144,145)(147,150)(148,149);
poly := sub<Sym(150)|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, 
s3*s2*s1*s3*s2*s3*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*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*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*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*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*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

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