Polytope of Type {6,50}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,50}*600
Also Known As : {6,50|2}. if this polytope has another name.
Group : SmallGroup(600,39)
Rank : 3
Schlafli Type : {6,50}
Number of vertices, edges, etc : 6, 150, 50
Order of s₀s₁s₂ : 150
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,50,2} of size 1200
Vertex Figure Of :
   {2,6,50} of size 1200
   {3,6,50} of size 1800
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,50}*200
   5-fold quotients : {6,10}*120
   6-fold quotients : {2,25}*100
   15-fold quotients : {2,10}*40
   25-fold quotients : {6,2}*24
   30-fold quotients : {2,5}*20
   50-fold quotients : {3,2}*12
   75-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,50}*1200, {6,100}*1200a
   3-fold covers : {18,50}*1800, {6,150}*1800a, {6,150}*1800b
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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

Finitely Presented Group Representation (Magma) :

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

References : None.
to this polytope