Polytope of Type {2,50,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,50,6}*1200
if this polytope has a name.
Group : SmallGroup(1200,203)
Rank : 4
Schlafli Type : {2,50,6}
Number of vertices, edges, etc : 2, 50, 150, 6
Order of s₀s₁s₂s₃ : 150
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 : {2,50,2}*400
   5-fold quotients : {2,10,6}*240
   6-fold quotients : {2,25,2}*200
   15-fold quotients : {2,10,2}*80
   25-fold quotients : {2,2,6}*48
   30-fold quotients : {2,5,2}*40
   50-fold quotients : {2,2,3}*24
   75-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4,  7)(  5,  6)(  8, 27)(  9, 26)( 10, 25)( 11, 24)( 12, 23)( 13, 22)
( 14, 21)( 15, 20)( 16, 19)( 17, 18)( 29, 32)( 30, 31)( 33, 52)( 34, 51)
( 35, 50)( 36, 49)( 37, 48)( 38, 47)( 39, 46)( 40, 45)( 41, 44)( 42, 43)
( 54, 57)( 55, 56)( 58, 77)( 59, 76)( 60, 75)( 61, 74)( 62, 73)( 63, 72)
( 64, 71)( 65, 70)( 66, 69)( 67, 68)( 79, 82)( 80, 81)( 83,102)( 84,101)
( 85,100)( 86, 99)( 87, 98)( 88, 97)( 89, 96)( 90, 95)( 91, 94)( 92, 93)
(104,107)(105,106)(108,127)(109,126)(110,125)(111,124)(112,123)(113,122)
(114,121)(115,120)(116,119)(117,118)(129,132)(130,131)(133,152)(134,151)
(135,150)(136,149)(137,148)(138,147)(139,146)(140,145)(141,144)(142,143);;
s2 := (  3,  8)(  4, 12)(  5, 11)(  6, 10)(  7,  9)( 13, 27)( 14, 26)( 15, 25)
( 16, 24)( 17, 23)( 18, 22)( 19, 21)( 28, 58)( 29, 62)( 30, 61)( 31, 60)
( 32, 59)( 33, 53)( 34, 57)( 35, 56)( 36, 55)( 37, 54)( 38, 77)( 39, 76)
( 40, 75)( 41, 74)( 42, 73)( 43, 72)( 44, 71)( 45, 70)( 46, 69)( 47, 68)
( 48, 67)( 49, 66)( 50, 65)( 51, 64)( 52, 63)( 78, 83)( 79, 87)( 80, 86)
( 81, 85)( 82, 84)( 88,102)( 89,101)( 90,100)( 91, 99)( 92, 98)( 93, 97)
( 94, 96)(103,133)(104,137)(105,136)(106,135)(107,134)(108,128)(109,132)
(110,131)(111,130)(112,129)(113,152)(114,151)(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);;
s3 := (  3,103)(  4,104)(  5,105)(  6,106)(  7,107)(  8,108)(  9,109)( 10,110)
( 11,111)( 12,112)( 13,113)( 14,114)( 15,115)( 16,116)( 17,117)( 18,118)
( 19,119)( 20,120)( 21,121)( 22,122)( 23,123)( 24,124)( 25,125)( 26,126)
( 27,127)( 28, 78)( 29, 79)( 30, 80)( 31, 81)( 32, 82)( 33, 83)( 34, 84)
( 35, 85)( 36, 86)( 37, 87)( 38, 88)( 39, 89)( 40, 90)( 41, 91)( 42, 92)
( 43, 93)( 44, 94)( 45, 95)( 46, 96)( 47, 97)( 48, 98)( 49, 99)( 50,100)
( 51,101)( 52,102)( 53,128)( 54,129)( 55,130)( 56,131)( 57,132)( 58,133)
( 59,134)( 60,135)( 61,136)( 62,137)( 63,138)( 64,139)( 65,140)( 66,141)
( 67,142)( 68,143)( 69,144)( 70,145)( 71,146)( 72,147)( 73,148)( 74,149)
( 75,150)( 76,151)( 77,152);;
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*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(152)!(1,2);
s1 := Sym(152)!(  4,  7)(  5,  6)(  8, 27)(  9, 26)( 10, 25)( 11, 24)( 12, 23)
( 13, 22)( 14, 21)( 15, 20)( 16, 19)( 17, 18)( 29, 32)( 30, 31)( 33, 52)
( 34, 51)( 35, 50)( 36, 49)( 37, 48)( 38, 47)( 39, 46)( 40, 45)( 41, 44)
( 42, 43)( 54, 57)( 55, 56)( 58, 77)( 59, 76)( 60, 75)( 61, 74)( 62, 73)
( 63, 72)( 64, 71)( 65, 70)( 66, 69)( 67, 68)( 79, 82)( 80, 81)( 83,102)
( 84,101)( 85,100)( 86, 99)( 87, 98)( 88, 97)( 89, 96)( 90, 95)( 91, 94)
( 92, 93)(104,107)(105,106)(108,127)(109,126)(110,125)(111,124)(112,123)
(113,122)(114,121)(115,120)(116,119)(117,118)(129,132)(130,131)(133,152)
(134,151)(135,150)(136,149)(137,148)(138,147)(139,146)(140,145)(141,144)
(142,143);
s2 := Sym(152)!(  3,  8)(  4, 12)(  5, 11)(  6, 10)(  7,  9)( 13, 27)( 14, 26)
( 15, 25)( 16, 24)( 17, 23)( 18, 22)( 19, 21)( 28, 58)( 29, 62)( 30, 61)
( 31, 60)( 32, 59)( 33, 53)( 34, 57)( 35, 56)( 36, 55)( 37, 54)( 38, 77)
( 39, 76)( 40, 75)( 41, 74)( 42, 73)( 43, 72)( 44, 71)( 45, 70)( 46, 69)
( 47, 68)( 48, 67)( 49, 66)( 50, 65)( 51, 64)( 52, 63)( 78, 83)( 79, 87)
( 80, 86)( 81, 85)( 82, 84)( 88,102)( 89,101)( 90,100)( 91, 99)( 92, 98)
( 93, 97)( 94, 96)(103,133)(104,137)(105,136)(106,135)(107,134)(108,128)
(109,132)(110,131)(111,130)(112,129)(113,152)(114,151)(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);
s3 := Sym(152)!(  3,103)(  4,104)(  5,105)(  6,106)(  7,107)(  8,108)(  9,109)
( 10,110)( 11,111)( 12,112)( 13,113)( 14,114)( 15,115)( 16,116)( 17,117)
( 18,118)( 19,119)( 20,120)( 21,121)( 22,122)( 23,123)( 24,124)( 25,125)
( 26,126)( 27,127)( 28, 78)( 29, 79)( 30, 80)( 31, 81)( 32, 82)( 33, 83)
( 34, 84)( 35, 85)( 36, 86)( 37, 87)( 38, 88)( 39, 89)( 40, 90)( 41, 91)
( 42, 92)( 43, 93)( 44, 94)( 45, 95)( 46, 96)( 47, 97)( 48, 98)( 49, 99)
( 50,100)( 51,101)( 52,102)( 53,128)( 54,129)( 55,130)( 56,131)( 57,132)
( 58,133)( 59,134)( 60,135)( 61,136)( 62,137)( 63,138)( 64,139)( 65,140)
( 66,141)( 67,142)( 68,143)( 69,144)( 70,145)( 71,146)( 72,147)( 73,148)
( 74,149)( 75,150)( 76,151)( 77,152);
poly := sub<Sym(152)|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*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 >;

to this polytope