Polytope of Type {50,6,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {50,6,3}*1800
if this polytope has a name.
Group : SmallGroup(1800,229)
Rank : 4
Schlafli Type : {50,6,3}
Number of vertices, edges, etc : 50, 150, 9, 3
Order of s0s1s2s3 : 150
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) :
3-fold quotients : {50,2,3}*600
5-fold quotients : {10,6,3}*360
6-fold quotients : {25,2,3}*300
15-fold quotients : {10,2,3}*120
25-fold quotients : {2,6,3}*72
30-fold quotients : {5,2,3}*60
75-fold quotients : {2,2,3}*24
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)( 77, 80)( 78, 79)( 81, 97)( 82, 96)
( 83,100)( 84, 99)( 85, 98)( 86, 92)( 87, 91)( 88, 95)( 89, 94)( 90, 93)
(102,105)(103,104)(106,122)(107,121)(108,125)(109,124)(110,123)(111,117)
(112,116)(113,120)(114,119)(115,118)(127,130)(128,129)(131,147)(132,146)
(133,150)(134,149)(135,148)(136,142)(137,141)(138,145)(139,144)(140,143)
(152,155)(153,154)(156,172)(157,171)(158,175)(159,174)(160,173)(161,167)
(162,166)(163,170)(164,169)(165,168)(177,180)(178,179)(181,197)(182,196)
(183,200)(184,199)(185,198)(186,192)(187,191)(188,195)(189,194)(190,193)
(202,205)(203,204)(206,222)(207,221)(208,225)(209,224)(210,223)(211,217)
(212,216)(213,220)(214,219)(215,218);;
s1 := ( 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);;
s2 := ( 1, 76)( 2, 77)( 3, 78)( 4, 79)( 5, 80)( 6, 81)( 7, 82)( 8, 83)
( 9, 84)( 10, 85)( 11, 86)( 12, 87)( 13, 88)( 14, 89)( 15, 90)( 16, 91)
( 17, 92)( 18, 93)( 19, 94)( 20, 95)( 21, 96)( 22, 97)( 23, 98)( 24, 99)
( 25,100)( 26,126)( 27,127)( 28,128)( 29,129)( 30,130)( 31,131)( 32,132)
( 33,133)( 34,134)( 35,135)( 36,136)( 37,137)( 38,138)( 39,139)( 40,140)
( 41,141)( 42,142)( 43,143)( 44,144)( 45,145)( 46,146)( 47,147)( 48,148)
( 49,149)( 50,150)( 51,101)( 52,102)( 53,103)( 54,104)( 55,105)( 56,106)
( 57,107)( 58,108)( 59,109)( 60,110)( 61,111)( 62,112)( 63,113)( 64,114)
( 65,115)( 66,116)( 67,117)( 68,118)( 69,119)( 70,120)( 71,121)( 72,122)
( 73,123)( 74,124)( 75,125)(176,201)(177,202)(178,203)(179,204)(180,205)
(181,206)(182,207)(183,208)(184,209)(185,210)(186,211)(187,212)(188,213)
(189,214)(190,215)(191,216)(192,217)(193,218)(194,219)(195,220)(196,221)
(197,222)(198,223)(199,224)(200,225);;
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)( 76,176)( 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,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, s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s3*s1*s2*s1*s2*s3*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*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*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)( 77, 80)( 78, 79)( 81, 97)
( 82, 96)( 83,100)( 84, 99)( 85, 98)( 86, 92)( 87, 91)( 88, 95)( 89, 94)
( 90, 93)(102,105)(103,104)(106,122)(107,121)(108,125)(109,124)(110,123)
(111,117)(112,116)(113,120)(114,119)(115,118)(127,130)(128,129)(131,147)
(132,146)(133,150)(134,149)(135,148)(136,142)(137,141)(138,145)(139,144)
(140,143)(152,155)(153,154)(156,172)(157,171)(158,175)(159,174)(160,173)
(161,167)(162,166)(163,170)(164,169)(165,168)(177,180)(178,179)(181,197)
(182,196)(183,200)(184,199)(185,198)(186,192)(187,191)(188,195)(189,194)
(190,193)(202,205)(203,204)(206,222)(207,221)(208,225)(209,224)(210,223)
(211,217)(212,216)(213,220)(214,219)(215,218);
s1 := 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);
s2 := Sym(225)!( 1, 76)( 2, 77)( 3, 78)( 4, 79)( 5, 80)( 6, 81)( 7, 82)
( 8, 83)( 9, 84)( 10, 85)( 11, 86)( 12, 87)( 13, 88)( 14, 89)( 15, 90)
( 16, 91)( 17, 92)( 18, 93)( 19, 94)( 20, 95)( 21, 96)( 22, 97)( 23, 98)
( 24, 99)( 25,100)( 26,126)( 27,127)( 28,128)( 29,129)( 30,130)( 31,131)
( 32,132)( 33,133)( 34,134)( 35,135)( 36,136)( 37,137)( 38,138)( 39,139)
( 40,140)( 41,141)( 42,142)( 43,143)( 44,144)( 45,145)( 46,146)( 47,147)
( 48,148)( 49,149)( 50,150)( 51,101)( 52,102)( 53,103)( 54,104)( 55,105)
( 56,106)( 57,107)( 58,108)( 59,109)( 60,110)( 61,111)( 62,112)( 63,113)
( 64,114)( 65,115)( 66,116)( 67,117)( 68,118)( 69,119)( 70,120)( 71,121)
( 72,122)( 73,123)( 74,124)( 75,125)(176,201)(177,202)(178,203)(179,204)
(180,205)(181,206)(182,207)(183,208)(184,209)(185,210)(186,211)(187,212)
(188,213)(189,214)(190,215)(191,216)(192,217)(193,218)(194,219)(195,220)
(196,221)(197,222)(198,223)(199,224)(200,225);
s3 := 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,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,
s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1,
s3*s1*s2*s1*s2*s3*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*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*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