Polytope of Type {2,6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,6}*1200a
if this polytope has a name.
Group : SmallGroup(1200,980)
Rank : 4
Schlafli Type : {2,6,6}
Number of vertices, edges, etc : 2, 50, 150, 50
Order of s₀s₁s₂s₃ : 10
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 : {2,6,3}*600
   75-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope