Polytope of Type {10,10,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,10,6}*1200c
if this polytope has a name.
Group : SmallGroup(1200,1006)
Rank : 4
Schlafli Type : {10,10,6}
Number of vertices, edges, etc : 10, 50, 30, 6
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) :
   2-fold quotients : {5,10,6}*600
   3-fold quotients : {10,10,2}*400c
   5-fold quotients : {10,2,6}*240
   6-fold quotients : {5,10,2}*200
   10-fold quotients : {5,2,6}*120, {10,2,3}*120
   15-fold quotients : {10,2,2}*80
   20-fold quotients : {5,2,3}*60
   25-fold quotients : {2,2,6}*48
   30-fold quotients : {5,2,2}*40
   50-fold quotients : {2,2,3}*24
   75-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope