Polytope of Type {10,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,6}*600b
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 : {10,3}*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 : {10,12}*1200a, {20,6}*1200b
   3-fold covers : {10,18}*1800a, {30,6}*1800a, {30,6}*1800c
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)(  2,124)(  3,117)(  4,115)(  5,108)(  6,114)(  7,107)(  8,105)
(  9,123)( 10,116)( 11,122)( 12,120)( 13,113)( 14,106)( 15,104)( 16,110)
( 17,103)( 18,121)( 19,119)( 20,112)( 21,118)( 22,111)( 23,109)( 24,102)
( 25,125)( 26, 76)( 27, 99)( 28, 92)( 29, 90)( 30, 83)( 31, 89)( 32, 82)
( 33, 80)( 34, 98)( 35, 91)( 36, 97)( 37, 95)( 38, 88)( 39, 81)( 40, 79)
( 41, 85)( 42, 78)( 43, 96)( 44, 94)( 45, 87)( 46, 93)( 47, 86)( 48, 84)
( 49, 77)( 50,100)( 51,126)( 52,149)( 53,142)( 54,140)( 55,133)( 56,139)
( 57,132)( 58,130)( 59,148)( 60,141)( 61,147)( 62,145)( 63,138)( 64,131)
( 65,129)( 66,135)( 67,128)( 68,146)( 69,144)( 70,137)( 71,143)( 72,136)
( 73,134)( 74,127)( 75,150);;
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, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s2*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)(  2,124)(  3,117)(  4,115)(  5,108)(  6,114)(  7,107)
(  8,105)(  9,123)( 10,116)( 11,122)( 12,120)( 13,113)( 14,106)( 15,104)
( 16,110)( 17,103)( 18,121)( 19,119)( 20,112)( 21,118)( 22,111)( 23,109)
( 24,102)( 25,125)( 26, 76)( 27, 99)( 28, 92)( 29, 90)( 30, 83)( 31, 89)
( 32, 82)( 33, 80)( 34, 98)( 35, 91)( 36, 97)( 37, 95)( 38, 88)( 39, 81)
( 40, 79)( 41, 85)( 42, 78)( 43, 96)( 44, 94)( 45, 87)( 46, 93)( 47, 86)
( 48, 84)( 49, 77)( 50,100)( 51,126)( 52,149)( 53,142)( 54,140)( 55,133)
( 56,139)( 57,132)( 58,130)( 59,148)( 60,141)( 61,147)( 62,145)( 63,138)
( 64,131)( 65,129)( 66,135)( 67,128)( 68,146)( 69,144)( 70,137)( 71,143)
( 72,136)( 73,134)( 74,127)( 75,150);
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, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
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