Polytope of Type {12,50}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,50}*1200
Also Known As : {12,50|2}. if this polytope has another name.
Group : SmallGroup(1200,130)
Rank : 3
Schlafli Type : {12,50}
Number of vertices, edges, etc : 12, 300, 50
Order of s0s1s2 : 300
Order of s0s1s2s1 : 2
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) :
2-fold quotients : {6,50}*600
3-fold quotients : {4,50}*400
5-fold quotients : {12,10}*240
6-fold quotients : {2,50}*200
10-fold quotients : {6,10}*120
12-fold quotients : {2,25}*100
15-fold quotients : {4,10}*80
25-fold quotients : {12,2}*48
30-fold quotients : {2,10}*40
50-fold quotients : {6,2}*24
60-fold quotients : {2,5}*20
75-fold quotients : {4,2}*16
100-fold quotients : {3,2}*12
150-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)(101,126)(102,127)(103,128)(104,129)(105,130)(106,131)(107,132)
(108,133)(109,134)(110,135)(111,136)(112,137)(113,138)(114,139)(115,140)
(116,141)(117,142)(118,143)(119,144)(120,145)(121,146)(122,147)(123,148)
(124,149)(125,150)(151,226)(152,227)(153,228)(154,229)(155,230)(156,231)
(157,232)(158,233)(159,234)(160,235)(161,236)(162,237)(163,238)(164,239)
(165,240)(166,241)(167,242)(168,243)(169,244)(170,245)(171,246)(172,247)
(173,248)(174,249)(175,250)(176,276)(177,277)(178,278)(179,279)(180,280)
(181,281)(182,282)(183,283)(184,284)(185,285)(186,286)(187,287)(188,288)
(189,289)(190,290)(191,291)(192,292)(193,293)(194,294)(195,295)(196,296)
(197,297)(198,298)(199,299)(200,300)(201,251)(202,252)(203,253)(204,254)
(205,255)(206,256)(207,257)(208,258)(209,259)(210,260)(211,261)(212,262)
(213,263)(214,264)(215,265)(216,266)(217,267)(218,268)(219,269)(220,270)
(221,271)(222,272)(223,273)(224,274)(225,275);;
s1 := ( 1,176)( 2,180)( 3,179)( 4,178)( 5,177)( 6,200)( 7,199)( 8,198)
( 9,197)( 10,196)( 11,195)( 12,194)( 13,193)( 14,192)( 15,191)( 16,190)
( 17,189)( 18,188)( 19,187)( 20,186)( 21,185)( 22,184)( 23,183)( 24,182)
( 25,181)( 26,151)( 27,155)( 28,154)( 29,153)( 30,152)( 31,175)( 32,174)
( 33,173)( 34,172)( 35,171)( 36,170)( 37,169)( 38,168)( 39,167)( 40,166)
( 41,165)( 42,164)( 43,163)( 44,162)( 45,161)( 46,160)( 47,159)( 48,158)
( 49,157)( 50,156)( 51,201)( 52,205)( 53,204)( 54,203)( 55,202)( 56,225)
( 57,224)( 58,223)( 59,222)( 60,221)( 61,220)( 62,219)( 63,218)( 64,217)
( 65,216)( 66,215)( 67,214)( 68,213)( 69,212)( 70,211)( 71,210)( 72,209)
( 73,208)( 74,207)( 75,206)( 76,251)( 77,255)( 78,254)( 79,253)( 80,252)
( 81,275)( 82,274)( 83,273)( 84,272)( 85,271)( 86,270)( 87,269)( 88,268)
( 89,267)( 90,266)( 91,265)( 92,264)( 93,263)( 94,262)( 95,261)( 96,260)
( 97,259)( 98,258)( 99,257)(100,256)(101,226)(102,230)(103,229)(104,228)
(105,227)(106,250)(107,249)(108,248)(109,247)(110,246)(111,245)(112,244)
(113,243)(114,242)(115,241)(116,240)(117,239)(118,238)(119,237)(120,236)
(121,235)(122,234)(123,233)(124,232)(125,231)(126,276)(127,280)(128,279)
(129,278)(130,277)(131,300)(132,299)(133,298)(134,297)(135,296)(136,295)
(137,294)(138,293)(139,292)(140,291)(141,290)(142,289)(143,288)(144,287)
(145,286)(146,285)(147,284)(148,283)(149,282)(150,281);;
s2 := ( 1, 6)( 2, 10)( 3, 9)( 4, 8)( 5, 7)( 11, 25)( 12, 24)( 13, 23)
( 14, 22)( 15, 21)( 16, 20)( 17, 19)( 26, 31)( 27, 35)( 28, 34)( 29, 33)
( 30, 32)( 36, 50)( 37, 49)( 38, 48)( 39, 47)( 40, 46)( 41, 45)( 42, 44)
( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 61, 75)( 62, 74)( 63, 73)
( 64, 72)( 65, 71)( 66, 70)( 67, 69)( 76, 81)( 77, 85)( 78, 84)( 79, 83)
( 80, 82)( 86,100)( 87, 99)( 88, 98)( 89, 97)( 90, 96)( 91, 95)( 92, 94)
(101,106)(102,110)(103,109)(104,108)(105,107)(111,125)(112,124)(113,123)
(114,122)(115,121)(116,120)(117,119)(126,131)(127,135)(128,134)(129,133)
(130,132)(136,150)(137,149)(138,148)(139,147)(140,146)(141,145)(142,144)
(151,156)(152,160)(153,159)(154,158)(155,157)(161,175)(162,174)(163,173)
(164,172)(165,171)(166,170)(167,169)(176,181)(177,185)(178,184)(179,183)
(180,182)(186,200)(187,199)(188,198)(189,197)(190,196)(191,195)(192,194)
(201,206)(202,210)(203,209)(204,208)(205,207)(211,225)(212,224)(213,223)
(214,222)(215,221)(216,220)(217,219)(226,231)(227,235)(228,234)(229,233)
(230,232)(236,250)(237,249)(238,248)(239,247)(240,246)(241,245)(242,244)
(251,256)(252,260)(253,259)(254,258)(255,257)(261,275)(262,274)(263,273)
(264,272)(265,271)(266,270)(267,269)(276,281)(277,285)(278,284)(279,283)
(280,282)(286,300)(287,299)(288,298)(289,297)(290,296)(291,295)(292,294);;
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*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,
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*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(300)!( 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)(101,126)(102,127)(103,128)(104,129)(105,130)(106,131)
(107,132)(108,133)(109,134)(110,135)(111,136)(112,137)(113,138)(114,139)
(115,140)(116,141)(117,142)(118,143)(119,144)(120,145)(121,146)(122,147)
(123,148)(124,149)(125,150)(151,226)(152,227)(153,228)(154,229)(155,230)
(156,231)(157,232)(158,233)(159,234)(160,235)(161,236)(162,237)(163,238)
(164,239)(165,240)(166,241)(167,242)(168,243)(169,244)(170,245)(171,246)
(172,247)(173,248)(174,249)(175,250)(176,276)(177,277)(178,278)(179,279)
(180,280)(181,281)(182,282)(183,283)(184,284)(185,285)(186,286)(187,287)
(188,288)(189,289)(190,290)(191,291)(192,292)(193,293)(194,294)(195,295)
(196,296)(197,297)(198,298)(199,299)(200,300)(201,251)(202,252)(203,253)
(204,254)(205,255)(206,256)(207,257)(208,258)(209,259)(210,260)(211,261)
(212,262)(213,263)(214,264)(215,265)(216,266)(217,267)(218,268)(219,269)
(220,270)(221,271)(222,272)(223,273)(224,274)(225,275);
s1 := Sym(300)!( 1,176)( 2,180)( 3,179)( 4,178)( 5,177)( 6,200)( 7,199)
( 8,198)( 9,197)( 10,196)( 11,195)( 12,194)( 13,193)( 14,192)( 15,191)
( 16,190)( 17,189)( 18,188)( 19,187)( 20,186)( 21,185)( 22,184)( 23,183)
( 24,182)( 25,181)( 26,151)( 27,155)( 28,154)( 29,153)( 30,152)( 31,175)
( 32,174)( 33,173)( 34,172)( 35,171)( 36,170)( 37,169)( 38,168)( 39,167)
( 40,166)( 41,165)( 42,164)( 43,163)( 44,162)( 45,161)( 46,160)( 47,159)
( 48,158)( 49,157)( 50,156)( 51,201)( 52,205)( 53,204)( 54,203)( 55,202)
( 56,225)( 57,224)( 58,223)( 59,222)( 60,221)( 61,220)( 62,219)( 63,218)
( 64,217)( 65,216)( 66,215)( 67,214)( 68,213)( 69,212)( 70,211)( 71,210)
( 72,209)( 73,208)( 74,207)( 75,206)( 76,251)( 77,255)( 78,254)( 79,253)
( 80,252)( 81,275)( 82,274)( 83,273)( 84,272)( 85,271)( 86,270)( 87,269)
( 88,268)( 89,267)( 90,266)( 91,265)( 92,264)( 93,263)( 94,262)( 95,261)
( 96,260)( 97,259)( 98,258)( 99,257)(100,256)(101,226)(102,230)(103,229)
(104,228)(105,227)(106,250)(107,249)(108,248)(109,247)(110,246)(111,245)
(112,244)(113,243)(114,242)(115,241)(116,240)(117,239)(118,238)(119,237)
(120,236)(121,235)(122,234)(123,233)(124,232)(125,231)(126,276)(127,280)
(128,279)(129,278)(130,277)(131,300)(132,299)(133,298)(134,297)(135,296)
(136,295)(137,294)(138,293)(139,292)(140,291)(141,290)(142,289)(143,288)
(144,287)(145,286)(146,285)(147,284)(148,283)(149,282)(150,281);
s2 := Sym(300)!( 1, 6)( 2, 10)( 3, 9)( 4, 8)( 5, 7)( 11, 25)( 12, 24)
( 13, 23)( 14, 22)( 15, 21)( 16, 20)( 17, 19)( 26, 31)( 27, 35)( 28, 34)
( 29, 33)( 30, 32)( 36, 50)( 37, 49)( 38, 48)( 39, 47)( 40, 46)( 41, 45)
( 42, 44)( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 61, 75)( 62, 74)
( 63, 73)( 64, 72)( 65, 71)( 66, 70)( 67, 69)( 76, 81)( 77, 85)( 78, 84)
( 79, 83)( 80, 82)( 86,100)( 87, 99)( 88, 98)( 89, 97)( 90, 96)( 91, 95)
( 92, 94)(101,106)(102,110)(103,109)(104,108)(105,107)(111,125)(112,124)
(113,123)(114,122)(115,121)(116,120)(117,119)(126,131)(127,135)(128,134)
(129,133)(130,132)(136,150)(137,149)(138,148)(139,147)(140,146)(141,145)
(142,144)(151,156)(152,160)(153,159)(154,158)(155,157)(161,175)(162,174)
(163,173)(164,172)(165,171)(166,170)(167,169)(176,181)(177,185)(178,184)
(179,183)(180,182)(186,200)(187,199)(188,198)(189,197)(190,196)(191,195)
(192,194)(201,206)(202,210)(203,209)(204,208)(205,207)(211,225)(212,224)
(213,223)(214,222)(215,221)(216,220)(217,219)(226,231)(227,235)(228,234)
(229,233)(230,232)(236,250)(237,249)(238,248)(239,247)(240,246)(241,245)
(242,244)(251,256)(252,260)(253,259)(254,258)(255,257)(261,275)(262,274)
(263,273)(264,272)(265,271)(266,270)(267,269)(276,281)(277,285)(278,284)
(279,283)(280,282)(286,300)(287,299)(288,298)(289,297)(290,296)(291,295)
(292,294);
poly := sub<Sym(300)|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*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,
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*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope