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Polytope of Type {2,6,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,10}*1200b
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 : {2,3,10}*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 := (  3,103)(  4,126)(  5,119)(  6,117)(  7,110)(  8,116)(  9,109)( 10,107)
( 11,125)( 12,118)( 13,124)( 14,122)( 15,115)( 16,108)( 17,106)( 18,112)
( 19,105)( 20,123)( 21,121)( 22,114)( 23,120)( 24,113)( 25,111)( 26,104)
( 27,127)( 28, 78)( 29,101)( 30, 94)( 31, 92)( 32, 85)( 33, 91)( 34, 84)
( 35, 82)( 36,100)( 37, 93)( 38, 99)( 39, 97)( 40, 90)( 41, 83)( 42, 81)
( 43, 87)( 44, 80)( 45, 98)( 46, 96)( 47, 89)( 48, 95)( 49, 88)( 50, 86)
( 51, 79)( 52,102)( 53,128)( 54,151)( 55,144)( 56,142)( 57,135)( 58,141)
( 59,134)( 60,132)( 61,150)( 62,143)( 63,149)( 64,147)( 65,140)( 66,133)
( 67,131)( 68,137)( 69,130)( 70,148)( 71,146)( 72,139)( 73,145)( 74,138)
( 75,136)( 76,129)( 77,152);;
s3 := (  3, 10)(  4,  9)(  5,  8)(  6, 12)(  7, 11)( 13, 25)( 14, 24)( 15, 23)
( 16, 27)( 17, 26)( 18, 20)( 21, 22)( 28, 35)( 29, 34)( 30, 33)( 31, 37)
( 32, 36)( 38, 50)( 39, 49)( 40, 48)( 41, 52)( 42, 51)( 43, 45)( 46, 47)
( 53, 60)( 54, 59)( 55, 58)( 56, 62)( 57, 61)( 63, 75)( 64, 74)( 65, 73)
( 66, 77)( 67, 76)( 68, 70)( 71, 72)( 78, 85)( 79, 84)( 80, 83)( 81, 87)
( 82, 86)( 88,100)( 89, 99)( 90, 98)( 91,102)( 92,101)( 93, 95)( 96, 97)
(103,110)(104,109)(105,108)(106,112)(107,111)(113,125)(114,124)(115,123)
(116,127)(117,126)(118,120)(121,122)(128,135)(129,134)(130,133)(131,137)
(132,136)(138,150)(139,149)(140,148)(141,152)(142,151)(143,145)(146,147);;
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*s1*s2*s1*s2*s3*s2*s1*s2, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*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)!(  3,103)(  4,126)(  5,119)(  6,117)(  7,110)(  8,116)(  9,109)
( 10,107)( 11,125)( 12,118)( 13,124)( 14,122)( 15,115)( 16,108)( 17,106)
( 18,112)( 19,105)( 20,123)( 21,121)( 22,114)( 23,120)( 24,113)( 25,111)
( 26,104)( 27,127)( 28, 78)( 29,101)( 30, 94)( 31, 92)( 32, 85)( 33, 91)
( 34, 84)( 35, 82)( 36,100)( 37, 93)( 38, 99)( 39, 97)( 40, 90)( 41, 83)
( 42, 81)( 43, 87)( 44, 80)( 45, 98)( 46, 96)( 47, 89)( 48, 95)( 49, 88)
( 50, 86)( 51, 79)( 52,102)( 53,128)( 54,151)( 55,144)( 56,142)( 57,135)
( 58,141)( 59,134)( 60,132)( 61,150)( 62,143)( 63,149)( 64,147)( 65,140)
( 66,133)( 67,131)( 68,137)( 69,130)( 70,148)( 71,146)( 72,139)( 73,145)
( 74,138)( 75,136)( 76,129)( 77,152);
s3 := Sym(152)!(  3, 10)(  4,  9)(  5,  8)(  6, 12)(  7, 11)( 13, 25)( 14, 24)
( 15, 23)( 16, 27)( 17, 26)( 18, 20)( 21, 22)( 28, 35)( 29, 34)( 30, 33)
( 31, 37)( 32, 36)( 38, 50)( 39, 49)( 40, 48)( 41, 52)( 42, 51)( 43, 45)
( 46, 47)( 53, 60)( 54, 59)( 55, 58)( 56, 62)( 57, 61)( 63, 75)( 64, 74)
( 65, 73)( 66, 77)( 67, 76)( 68, 70)( 71, 72)( 78, 85)( 79, 84)( 80, 83)
( 81, 87)( 82, 86)( 88,100)( 89, 99)( 90, 98)( 91,102)( 92,101)( 93, 95)
( 96, 97)(103,110)(104,109)(105,108)(106,112)(107,111)(113,125)(114,124)
(115,123)(116,127)(117,126)(118,120)(121,122)(128,135)(129,134)(130,133)
(131,137)(132,136)(138,150)(139,149)(140,148)(141,152)(142,151)(143,145)
(146,147);
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*s1*s2*s1*s2*s3*s2*s1*s2, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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