Polytope of Type {6,10,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,10,10}*1200c
if this polytope has a name.
Group : SmallGroup(1200,1006)
Rank : 4
Schlafli Type : {6,10,10}
Number of vertices, edges, etc : 6, 30, 50, 10
Order of s₀s₁s₂s₃ : 30
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   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) :
   3-fold quotients : {2,10,10}*400c
   5-fold quotients : {6,10,2}*240
   6-fold quotients : {2,5,10}*200
   15-fold quotients : {2,10,2}*80
   25-fold quotients : {6,2,2}*48
   30-fold quotients : {2,5,2}*40
   50-fold quotients : {3,2,2}*24
   75-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
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, 46)(  7, 50)(  8, 49)
(  9, 48)( 10, 47)( 11, 41)( 12, 45)( 13, 44)( 14, 43)( 15, 42)( 16, 36)
( 17, 40)( 18, 39)( 19, 38)( 20, 37)( 21, 31)( 22, 35)( 23, 34)( 24, 33)
( 25, 32)( 52, 55)( 53, 54)( 56, 71)( 57, 75)( 58, 74)( 59, 73)( 60, 72)
( 61, 66)( 62, 70)( 63, 69)( 64, 68)( 65, 67)( 76,101)( 77,105)( 78,104)
( 79,103)( 80,102)( 81,121)( 82,125)( 83,124)( 84,123)( 85,122)( 86,116)
( 87,120)( 88,119)( 89,118)( 90,117)( 91,111)( 92,115)( 93,114)( 94,113)
( 95,112)( 96,106)( 97,110)( 98,109)( 99,108)(100,107)(127,130)(128,129)
(131,146)(132,150)(133,149)(134,148)(135,147)(136,141)(137,145)(138,144)
(139,143)(140,142);;
s2 := (  1, 82)(  2, 81)(  3, 85)(  4, 84)(  5, 83)(  6, 77)(  7, 76)(  8, 80)
(  9, 79)( 10, 78)( 11, 97)( 12, 96)( 13,100)( 14, 99)( 15, 98)( 16, 92)
( 17, 91)( 18, 95)( 19, 94)( 20, 93)( 21, 87)( 22, 86)( 23, 90)( 24, 89)
( 25, 88)( 26,107)( 27,106)( 28,110)( 29,109)( 30,108)( 31,102)( 32,101)
( 33,105)( 34,104)( 35,103)( 36,122)( 37,121)( 38,125)( 39,124)( 40,123)
( 41,117)( 42,116)( 43,120)( 44,119)( 45,118)( 46,112)( 47,111)( 48,115)
( 49,114)( 50,113)( 51,132)( 52,131)( 53,135)( 54,134)( 55,133)( 56,127)
( 57,126)( 58,130)( 59,129)( 60,128)( 61,147)( 62,146)( 63,150)( 64,149)
( 65,148)( 66,142)( 67,141)( 68,145)( 69,144)( 70,143)( 71,137)( 72,136)
( 73,140)( 74,139)( 75,138);;
s3 := (  6, 21)(  7, 22)(  8, 23)(  9, 24)( 10, 25)( 11, 16)( 12, 17)( 13, 18)
( 14, 19)( 15, 20)( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)( 36, 41)
( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 56, 71)( 57, 72)( 58, 73)( 59, 74)
( 60, 75)( 61, 66)( 62, 67)( 63, 68)( 64, 69)( 65, 70)( 81, 96)( 82, 97)
( 83, 98)( 84, 99)( 85,100)( 86, 91)( 87, 92)( 88, 93)( 89, 94)( 90, 95)
(106,121)(107,122)(108,123)(109,124)(110,125)(111,116)(112,117)(113,118)
(114,119)(115,120)(131,146)(132,147)(133,148)(134,149)(135,150)(136,141)
(137,142)(138,143)(139,144)(140,145);;
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, s0*s1*s2*s1*s0*s1*s2*s1, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 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*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*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, 46)(  7, 50)
(  8, 49)(  9, 48)( 10, 47)( 11, 41)( 12, 45)( 13, 44)( 14, 43)( 15, 42)
( 16, 36)( 17, 40)( 18, 39)( 19, 38)( 20, 37)( 21, 31)( 22, 35)( 23, 34)
( 24, 33)( 25, 32)( 52, 55)( 53, 54)( 56, 71)( 57, 75)( 58, 74)( 59, 73)
( 60, 72)( 61, 66)( 62, 70)( 63, 69)( 64, 68)( 65, 67)( 76,101)( 77,105)
( 78,104)( 79,103)( 80,102)( 81,121)( 82,125)( 83,124)( 84,123)( 85,122)
( 86,116)( 87,120)( 88,119)( 89,118)( 90,117)( 91,111)( 92,115)( 93,114)
( 94,113)( 95,112)( 96,106)( 97,110)( 98,109)( 99,108)(100,107)(127,130)
(128,129)(131,146)(132,150)(133,149)(134,148)(135,147)(136,141)(137,145)
(138,144)(139,143)(140,142);
s2 := Sym(150)!(  1, 82)(  2, 81)(  3, 85)(  4, 84)(  5, 83)(  6, 77)(  7, 76)
(  8, 80)(  9, 79)( 10, 78)( 11, 97)( 12, 96)( 13,100)( 14, 99)( 15, 98)
( 16, 92)( 17, 91)( 18, 95)( 19, 94)( 20, 93)( 21, 87)( 22, 86)( 23, 90)
( 24, 89)( 25, 88)( 26,107)( 27,106)( 28,110)( 29,109)( 30,108)( 31,102)
( 32,101)( 33,105)( 34,104)( 35,103)( 36,122)( 37,121)( 38,125)( 39,124)
( 40,123)( 41,117)( 42,116)( 43,120)( 44,119)( 45,118)( 46,112)( 47,111)
( 48,115)( 49,114)( 50,113)( 51,132)( 52,131)( 53,135)( 54,134)( 55,133)
( 56,127)( 57,126)( 58,130)( 59,129)( 60,128)( 61,147)( 62,146)( 63,150)
( 64,149)( 65,148)( 66,142)( 67,141)( 68,145)( 69,144)( 70,143)( 71,137)
( 72,136)( 73,140)( 74,139)( 75,138);
s3 := Sym(150)!(  6, 21)(  7, 22)(  8, 23)(  9, 24)( 10, 25)( 11, 16)( 12, 17)
( 13, 18)( 14, 19)( 15, 20)( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)
( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 56, 71)( 57, 72)( 58, 73)
( 59, 74)( 60, 75)( 61, 66)( 62, 67)( 63, 68)( 64, 69)( 65, 70)( 81, 96)
( 82, 97)( 83, 98)( 84, 99)( 85,100)( 86, 91)( 87, 92)( 88, 93)( 89, 94)
( 90, 95)(106,121)(107,122)(108,123)(109,124)(110,125)(111,116)(112,117)
(113,118)(114,119)(115,120)(131,146)(132,147)(133,148)(134,149)(135,150)
(136,141)(137,142)(138,143)(139,144)(140,145);
poly := sub<Sym(150)|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, 
s0*s1*s2*s1*s0*s1*s2*s1, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
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*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope