Polytope of Type {3,6,50}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,6,50}*1800
if this polytope has a name.
Group : SmallGroup(1800,229)
Rank : 4
Schlafli Type : {3,6,50}
Number of vertices, edges, etc : 3, 9, 150, 50
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 : {3,2,50}*600
5-fold quotients : {3,6,10}*360
6-fold quotients : {3,2,25}*300
15-fold quotients : {3,2,10}*120
25-fold quotients : {3,6,2}*72
30-fold quotients : {3,2,5}*60
75-fold quotients : {3,2,2}*24
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)( 2,102)( 3,103)( 4,104)( 5,105)( 6,106)( 7,107)( 8,108)
( 9,109)( 10,110)( 11,111)( 12,112)( 13,113)( 14,114)( 15,115)( 16,116)
( 17,117)( 18,118)( 19,119)( 20,120)( 21,121)( 22,122)( 23,123)( 24,124)
( 25,125)( 26, 76)( 27, 77)( 28, 78)( 29, 79)( 30, 80)( 31, 81)( 32, 82)
( 33, 83)( 34, 84)( 35, 85)( 36, 86)( 37, 87)( 38, 88)( 39, 89)( 40, 90)
( 41, 91)( 42, 92)( 43, 93)( 44, 94)( 45, 95)( 46, 96)( 47, 97)( 48, 98)
( 49, 99)( 50,100)( 51,126)( 52,127)( 53,128)( 54,129)( 55,130)( 56,131)
( 57,132)( 58,133)( 59,134)( 60,135)( 61,136)( 62,137)( 63,138)( 64,139)
( 65,140)( 66,141)( 67,142)( 68,143)( 69,144)( 70,145)( 71,146)( 72,147)
( 73,148)( 74,149)( 75,150)(151,176)(152,177)(153,178)(154,179)(155,180)
(156,181)(157,182)(158,183)(159,184)(160,185)(161,186)(162,187)(163,188)
(164,189)(165,190)(166,191)(167,192)(168,193)(169,194)(170,195)(171,196)
(172,197)(173,198)(174,199)(175,200);;
s2 := ( 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);;
s3 := ( 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, 81)( 77, 85)( 78, 84)( 79, 83)
( 80, 82)( 86, 97)( 87, 96)( 88,100)( 89, 99)( 90, 98)( 91, 92)( 93, 95)
(101,106)(102,110)(103,109)(104,108)(105,107)(111,122)(112,121)(113,125)
(114,124)(115,123)(116,117)(118,120)(126,131)(127,135)(128,134)(129,133)
(130,132)(136,147)(137,146)(138,150)(139,149)(140,148)(141,142)(143,145)
(151,156)(152,160)(153,159)(154,158)(155,157)(161,172)(162,171)(163,175)
(164,174)(165,173)(166,167)(168,170)(176,181)(177,185)(178,184)(179,183)
(180,182)(186,197)(187,196)(188,200)(189,199)(190,198)(191,192)(193,195)
(201,206)(202,210)(203,209)(204,208)(205,207)(211,222)(212,221)(213,225)
(214,224)(215,223)(216,217)(218,220);;
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, s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
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)( 2,102)( 3,103)( 4,104)( 5,105)( 6,106)( 7,107)
( 8,108)( 9,109)( 10,110)( 11,111)( 12,112)( 13,113)( 14,114)( 15,115)
( 16,116)( 17,117)( 18,118)( 19,119)( 20,120)( 21,121)( 22,122)( 23,123)
( 24,124)( 25,125)( 26, 76)( 27, 77)( 28, 78)( 29, 79)( 30, 80)( 31, 81)
( 32, 82)( 33, 83)( 34, 84)( 35, 85)( 36, 86)( 37, 87)( 38, 88)( 39, 89)
( 40, 90)( 41, 91)( 42, 92)( 43, 93)( 44, 94)( 45, 95)( 46, 96)( 47, 97)
( 48, 98)( 49, 99)( 50,100)( 51,126)( 52,127)( 53,128)( 54,129)( 55,130)
( 56,131)( 57,132)( 58,133)( 59,134)( 60,135)( 61,136)( 62,137)( 63,138)
( 64,139)( 65,140)( 66,141)( 67,142)( 68,143)( 69,144)( 70,145)( 71,146)
( 72,147)( 73,148)( 74,149)( 75,150)(151,176)(152,177)(153,178)(154,179)
(155,180)(156,181)(157,182)(158,183)(159,184)(160,185)(161,186)(162,187)
(163,188)(164,189)(165,190)(166,191)(167,192)(168,193)(169,194)(170,195)
(171,196)(172,197)(173,198)(174,199)(175,200);
s2 := 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);
s3 := 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, 81)( 77, 85)( 78, 84)
( 79, 83)( 80, 82)( 86, 97)( 87, 96)( 88,100)( 89, 99)( 90, 98)( 91, 92)
( 93, 95)(101,106)(102,110)(103,109)(104,108)(105,107)(111,122)(112,121)
(113,125)(114,124)(115,123)(116,117)(118,120)(126,131)(127,135)(128,134)
(129,133)(130,132)(136,147)(137,146)(138,150)(139,149)(140,148)(141,142)
(143,145)(151,156)(152,160)(153,159)(154,158)(155,157)(161,172)(162,171)
(163,175)(164,174)(165,173)(166,167)(168,170)(176,181)(177,185)(178,184)
(179,183)(180,182)(186,197)(187,196)(188,200)(189,199)(190,198)(191,192)
(193,195)(201,206)(202,210)(203,209)(204,208)(205,207)(211,222)(212,221)
(213,225)(214,224)(215,223)(216,217)(218,220);
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,
s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope