Polytope of Type {2,74,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,74,4}*1184
if this polytope has a name.
Group : SmallGroup(1184,182)
Rank : 4
Schlafli Type : {2,74,4}
Number of vertices, edges, etc : 2, 74, 148, 4
Order of s₀s₁s₂s₃ : 148
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) :
   2-fold quotients : {2,74,2}*592
   4-fold quotients : {2,37,2}*296
   37-fold quotients : {2,2,4}*32
   74-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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