Polytope of Type {6,6,2}

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

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

Permutation Representation (Magma) :

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

to this polytope