Polytope of Type {2,6,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,10}*1200a
if this polytope has a name.
Group : SmallGroup(1200,980)
Rank : 4
Schlafli Type : {2,6,10}
Number of vertices, edges, etc : 2, 30, 150, 50
Order of s₀s₁s₂s₃ : 6
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 : {2,6,10}*600
   25-fold quotients : {2,6,2}*48
   50-fold quotients : {2,3,2}*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,  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, 84)(  5, 83)(  6, 87)(  7, 86)(  8, 80)(  9, 79)( 10, 78)
( 11, 82)( 12, 81)( 13,100)( 14, 99)( 15, 98)( 16,102)( 17,101)( 18, 95)
( 19, 94)( 20, 93)( 21, 97)( 22, 96)( 23, 90)( 24, 89)( 25, 88)( 26, 92)
( 27, 91)( 28,110)( 29,109)( 30,108)( 31,112)( 32,111)( 33,105)( 34,104)
( 35,103)( 36,107)( 37,106)( 38,125)( 39,124)( 40,123)( 41,127)( 42,126)
( 43,120)( 44,119)( 45,118)( 46,122)( 47,121)( 48,115)( 49,114)( 50,113)
( 51,117)( 52,116)( 53,135)( 54,134)( 55,133)( 56,137)( 57,136)( 58,130)
( 59,129)( 60,128)( 61,132)( 62,131)( 63,150)( 64,149)( 65,148)( 66,152)
( 67,151)( 68,145)( 69,144)( 70,143)( 71,147)( 72,146)( 73,140)( 74,139)
( 75,138)( 76,142)( 77,141);;
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, 
s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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, 84)(  5, 83)(  6, 87)(  7, 86)(  8, 80)(  9, 79)
( 10, 78)( 11, 82)( 12, 81)( 13,100)( 14, 99)( 15, 98)( 16,102)( 17,101)
( 18, 95)( 19, 94)( 20, 93)( 21, 97)( 22, 96)( 23, 90)( 24, 89)( 25, 88)
( 26, 92)( 27, 91)( 28,110)( 29,109)( 30,108)( 31,112)( 32,111)( 33,105)
( 34,104)( 35,103)( 36,107)( 37,106)( 38,125)( 39,124)( 40,123)( 41,127)
( 42,126)( 43,120)( 44,119)( 45,118)( 46,122)( 47,121)( 48,115)( 49,114)
( 50,113)( 51,117)( 52,116)( 53,135)( 54,134)( 55,133)( 56,137)( 57,136)
( 58,130)( 59,129)( 60,128)( 61,132)( 62,131)( 63,150)( 64,149)( 65,148)
( 66,152)( 67,151)( 68,145)( 69,144)( 70,143)( 71,147)( 72,146)( 73,140)
( 74,139)( 75,138)( 76,142)( 77,141);
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, 
s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope