Polytope of Type {10,6}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,6}*600a
if this polytope has a name.
Group : SmallGroup(600,154)
Rank : 3
Schlafli Type : {10,6}
Number of vertices, edges, etc : 50, 150, 30
Order of s₀s₁s₂ : 6
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {10,6,2} of size 1200
Vertex Figure Of :
   {2,10,6} of size 1200
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,6}*300
   25-fold quotients : {2,6}*24
   50-fold quotients : {2,3}*12
   75-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {20,6}*1200a, {10,12}*1200b
   3-fold covers : {10,18}*1800b, {30,6}*1800b, {30,6}*1800d
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1> of order 5.
      6 facets:
         6 of {10}*20
      10 vertex figures:
         10 of {6}*12
   P/N, where N=<s0*s1*s0*s1> of order 5.
      14 facets:
         10 of {2}*4
         4 of {10}*20
      10 vertex figures:
         10 of {6}*12

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

Finitely Presented Group Representation (GAP) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope

Polytope of Type {10,6}

Twisty Puzzle