Polytope of Type {6,150}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,150}*1800a
if this polytope has a name.
Group : SmallGroup(1800,229)
Rank : 3
Schlafli Type : {6,150}
Number of vertices, edges, etc : 6, 450, 150
Order of s₀s₁s₂ : 150
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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 : {6,50}*600
   5-fold quotients : {6,30}*360a
   9-fold quotients : {2,50}*200
   15-fold quotients : {6,10}*120
   18-fold quotients : {2,25}*100
   25-fold quotients : {6,6}*72c
   45-fold quotients : {2,10}*40
   50-fold quotients : {3,6}*36
   75-fold quotients : {6,2}*24
   90-fold quotients : {2,5}*20
   150-fold quotients : {3,2}*12
   225-fold quotients : {2,2}*8
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)( 76,151)( 77,152)( 78,153)( 79,154)( 80,155)( 81,156)( 82,157)
( 83,158)( 84,159)( 85,160)( 86,161)( 87,162)( 88,163)( 89,164)( 90,165)
( 91,166)( 92,167)( 93,168)( 94,169)( 95,170)( 96,171)( 97,172)( 98,173)
( 99,174)(100,175)(101,201)(102,202)(103,203)(104,204)(105,205)(106,206)
(107,207)(108,208)(109,209)(110,210)(111,211)(112,212)(113,213)(114,214)
(115,215)(116,216)(117,217)(118,218)(119,219)(120,220)(121,221)(122,222)
(123,223)(124,224)(125,225)(126,176)(127,177)(128,178)(129,179)(130,180)
(131,181)(132,182)(133,183)(134,184)(135,185)(136,186)(137,187)(138,188)
(139,189)(140,190)(141,191)(142,192)(143,193)(144,194)(145,195)(146,196)
(147,197)(148,198)(149,199)(150,200);;
s1 := (  1,101)(  2,105)(  3,104)(  4,103)(  5,102)(  6,122)(  7,121)(  8,125)
(  9,124)( 10,123)( 11,117)( 12,116)( 13,120)( 14,119)( 15,118)( 16,112)
( 17,111)( 18,115)( 19,114)( 20,113)( 21,107)( 22,106)( 23,110)( 24,109)
( 25,108)( 26, 76)( 27, 80)( 28, 79)( 29, 78)( 30, 77)( 31, 97)( 32, 96)
( 33,100)( 34, 99)( 35, 98)( 36, 92)( 37, 91)( 38, 95)( 39, 94)( 40, 93)
( 41, 87)( 42, 86)( 43, 90)( 44, 89)( 45, 88)( 46, 82)( 47, 81)( 48, 85)
( 49, 84)( 50, 83)( 51,126)( 52,130)( 53,129)( 54,128)( 55,127)( 56,147)
( 57,146)( 58,150)( 59,149)( 60,148)( 61,142)( 62,141)( 63,145)( 64,144)
( 65,143)( 66,137)( 67,136)( 68,140)( 69,139)( 70,138)( 71,132)( 72,131)
( 73,135)( 74,134)( 75,133)(151,176)(152,180)(153,179)(154,178)(155,177)
(156,197)(157,196)(158,200)(159,199)(160,198)(161,192)(162,191)(163,195)
(164,194)(165,193)(166,187)(167,186)(168,190)(169,189)(170,188)(171,182)
(172,181)(173,185)(174,184)(175,183)(202,205)(203,204)(206,222)(207,221)
(208,225)(209,224)(210,223)(211,217)(212,216)(213,220)(214,219)(215,218);;
s2 := (  1,  6)(  2, 10)(  3,  9)(  4,  8)(  5,  7)( 11, 22)( 12, 21)( 13, 25)
( 14, 24)( 15, 23)( 16, 17)( 18, 20)( 26, 31)( 27, 35)( 28, 34)( 29, 33)
( 30, 32)( 36, 47)( 37, 46)( 38, 50)( 39, 49)( 40, 48)( 41, 42)( 43, 45)
( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 61, 72)( 62, 71)( 63, 75)
( 64, 74)( 65, 73)( 66, 67)( 68, 70)( 76,156)( 77,160)( 78,159)( 79,158)
( 80,157)( 81,151)( 82,155)( 83,154)( 84,153)( 85,152)( 86,172)( 87,171)
( 88,175)( 89,174)( 90,173)( 91,167)( 92,166)( 93,170)( 94,169)( 95,168)
( 96,162)( 97,161)( 98,165)( 99,164)(100,163)(101,181)(102,185)(103,184)
(104,183)(105,182)(106,176)(107,180)(108,179)(109,178)(110,177)(111,197)
(112,196)(113,200)(114,199)(115,198)(116,192)(117,191)(118,195)(119,194)
(120,193)(121,187)(122,186)(123,190)(124,189)(125,188)(126,206)(127,210)
(128,209)(129,208)(130,207)(131,201)(132,205)(133,204)(134,203)(135,202)
(136,222)(137,221)(138,225)(139,224)(140,223)(141,217)(142,216)(143,220)
(144,219)(145,218)(146,212)(147,211)(148,215)(149,214)(150,213);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(225)!( 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)( 76,151)( 77,152)( 78,153)( 79,154)( 80,155)( 81,156)
( 82,157)( 83,158)( 84,159)( 85,160)( 86,161)( 87,162)( 88,163)( 89,164)
( 90,165)( 91,166)( 92,167)( 93,168)( 94,169)( 95,170)( 96,171)( 97,172)
( 98,173)( 99,174)(100,175)(101,201)(102,202)(103,203)(104,204)(105,205)
(106,206)(107,207)(108,208)(109,209)(110,210)(111,211)(112,212)(113,213)
(114,214)(115,215)(116,216)(117,217)(118,218)(119,219)(120,220)(121,221)
(122,222)(123,223)(124,224)(125,225)(126,176)(127,177)(128,178)(129,179)
(130,180)(131,181)(132,182)(133,183)(134,184)(135,185)(136,186)(137,187)
(138,188)(139,189)(140,190)(141,191)(142,192)(143,193)(144,194)(145,195)
(146,196)(147,197)(148,198)(149,199)(150,200);
s1 := Sym(225)!(  1,101)(  2,105)(  3,104)(  4,103)(  5,102)(  6,122)(  7,121)
(  8,125)(  9,124)( 10,123)( 11,117)( 12,116)( 13,120)( 14,119)( 15,118)
( 16,112)( 17,111)( 18,115)( 19,114)( 20,113)( 21,107)( 22,106)( 23,110)
( 24,109)( 25,108)( 26, 76)( 27, 80)( 28, 79)( 29, 78)( 30, 77)( 31, 97)
( 32, 96)( 33,100)( 34, 99)( 35, 98)( 36, 92)( 37, 91)( 38, 95)( 39, 94)
( 40, 93)( 41, 87)( 42, 86)( 43, 90)( 44, 89)( 45, 88)( 46, 82)( 47, 81)
( 48, 85)( 49, 84)( 50, 83)( 51,126)( 52,130)( 53,129)( 54,128)( 55,127)
( 56,147)( 57,146)( 58,150)( 59,149)( 60,148)( 61,142)( 62,141)( 63,145)
( 64,144)( 65,143)( 66,137)( 67,136)( 68,140)( 69,139)( 70,138)( 71,132)
( 72,131)( 73,135)( 74,134)( 75,133)(151,176)(152,180)(153,179)(154,178)
(155,177)(156,197)(157,196)(158,200)(159,199)(160,198)(161,192)(162,191)
(163,195)(164,194)(165,193)(166,187)(167,186)(168,190)(169,189)(170,188)
(171,182)(172,181)(173,185)(174,184)(175,183)(202,205)(203,204)(206,222)
(207,221)(208,225)(209,224)(210,223)(211,217)(212,216)(213,220)(214,219)
(215,218);
s2 := Sym(225)!(  1,  6)(  2, 10)(  3,  9)(  4,  8)(  5,  7)( 11, 22)( 12, 21)
( 13, 25)( 14, 24)( 15, 23)( 16, 17)( 18, 20)( 26, 31)( 27, 35)( 28, 34)
( 29, 33)( 30, 32)( 36, 47)( 37, 46)( 38, 50)( 39, 49)( 40, 48)( 41, 42)
( 43, 45)( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 61, 72)( 62, 71)
( 63, 75)( 64, 74)( 65, 73)( 66, 67)( 68, 70)( 76,156)( 77,160)( 78,159)
( 79,158)( 80,157)( 81,151)( 82,155)( 83,154)( 84,153)( 85,152)( 86,172)
( 87,171)( 88,175)( 89,174)( 90,173)( 91,167)( 92,166)( 93,170)( 94,169)
( 95,168)( 96,162)( 97,161)( 98,165)( 99,164)(100,163)(101,181)(102,185)
(103,184)(104,183)(105,182)(106,176)(107,180)(108,179)(109,178)(110,177)
(111,197)(112,196)(113,200)(114,199)(115,198)(116,192)(117,191)(118,195)
(119,194)(120,193)(121,187)(122,186)(123,190)(124,189)(125,188)(126,206)
(127,210)(128,209)(129,208)(130,207)(131,201)(132,205)(133,204)(134,203)
(135,202)(136,222)(137,221)(138,225)(139,224)(140,223)(141,217)(142,216)
(143,220)(144,219)(145,218)(146,212)(147,211)(148,215)(149,214)(150,213);
poly := sub<Sym(225)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1 >;

References : None.
to this polytope