Polytope of Type {150,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {150,6}*1800a
if this polytope has a name.
Group : SmallGroup(1800,229)
Rank : 3
Schlafli Type : {150,6}
Number of vertices, edges, etc : 150, 450, 6
Order of s₀s₁s₂ : 150
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {50,6}*600
   5-fold quotients : {30,6}*360a
   9-fold quotients : {50,2}*200
   15-fold quotients : {10,6}*120
   18-fold quotients : {25,2}*100
   25-fold quotients : {6,6}*72b
   45-fold quotients : {10,2}*40
   50-fold quotients : {6,3}*36
   75-fold quotients : {2,6}*24
   90-fold quotients : {5,2}*20
   150-fold quotients : {2,3}*12
   225-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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