Polytope of Type {150,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {150,4}*1200a
Also Known As : {150,4|2}. if this polytope has another name.
Group : SmallGroup(1200,173)
Rank : 3
Schlafli Type : {150,4}
Number of vertices, edges, etc : 150, 300, 4
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 : {150,2}*600
3-fold quotients : {50,4}*400
4-fold quotients : {75,2}*300
5-fold quotients : {30,4}*240a
6-fold quotients : {50,2}*200
10-fold quotients : {30,2}*120
12-fold quotients : {25,2}*100
15-fold quotients : {10,4}*80
20-fold quotients : {15,2}*60
25-fold quotients : {6,4}*48a
30-fold quotients : {10,2}*40
50-fold quotients : {6,2}*24
60-fold quotients : {5,2}*20
75-fold quotients : {2,4}*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 := ( 2, 5)( 3, 4)( 6, 25)( 7, 24)( 8, 23)( 9, 22)( 10, 21)( 11, 20)
( 12, 19)( 13, 18)( 14, 17)( 15, 16)( 26, 51)( 27, 55)( 28, 54)( 29, 53)
( 30, 52)( 31, 75)( 32, 74)( 33, 73)( 34, 72)( 35, 71)( 36, 70)( 37, 69)
( 38, 68)( 39, 67)( 40, 66)( 41, 65)( 42, 64)( 43, 63)( 44, 62)( 45, 61)
( 46, 60)( 47, 59)( 48, 58)( 49, 57)( 50, 56)( 77, 80)( 78, 79)( 81,100)
( 82, 99)( 83, 98)( 84, 97)( 85, 96)( 86, 95)( 87, 94)( 88, 93)( 89, 92)
( 90, 91)(101,126)(102,130)(103,129)(104,128)(105,127)(106,150)(107,149)
(108,148)(109,147)(110,146)(111,145)(112,144)(113,143)(114,142)(115,141)
(116,140)(117,139)(118,138)(119,137)(120,136)(121,135)(122,134)(123,133)
(124,132)(125,131)(152,155)(153,154)(156,175)(157,174)(158,173)(159,172)
(160,171)(161,170)(162,169)(163,168)(164,167)(165,166)(176,201)(177,205)
(178,204)(179,203)(180,202)(181,225)(182,224)(183,223)(184,222)(185,221)
(186,220)(187,219)(188,218)(189,217)(190,216)(191,215)(192,214)(193,213)
(194,212)(195,211)(196,210)(197,209)(198,208)(199,207)(200,206)(227,230)
(228,229)(231,250)(232,249)(233,248)(234,247)(235,246)(236,245)(237,244)
(238,243)(239,242)(240,241)(251,276)(252,280)(253,279)(254,278)(255,277)
(256,300)(257,299)(258,298)(259,297)(260,296)(261,295)(262,294)(263,293)
(264,292)(265,291)(266,290)(267,289)(268,288)(269,287)(270,286)(271,285)
(272,284)(273,283)(274,282)(275,281);;
s1 := ( 1, 31)( 2, 35)( 3, 34)( 4, 33)( 5, 32)( 6, 26)( 7, 30)( 8, 29)
( 9, 28)( 10, 27)( 11, 50)( 12, 49)( 13, 48)( 14, 47)( 15, 46)( 16, 45)
( 17, 44)( 18, 43)( 19, 42)( 20, 41)( 21, 40)( 22, 39)( 23, 38)( 24, 37)
( 25, 36)( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 61, 75)( 62, 74)
( 63, 73)( 64, 72)( 65, 71)( 66, 70)( 67, 69)( 76,106)( 77,110)( 78,109)
( 79,108)( 80,107)( 81,101)( 82,105)( 83,104)( 84,103)( 85,102)( 86,125)
( 87,124)( 88,123)( 89,122)( 90,121)( 91,120)( 92,119)( 93,118)( 94,117)
( 95,116)( 96,115)( 97,114)( 98,113)( 99,112)(100,111)(126,131)(127,135)
(128,134)(129,133)(130,132)(136,150)(137,149)(138,148)(139,147)(140,146)
(141,145)(142,144)(151,256)(152,260)(153,259)(154,258)(155,257)(156,251)
(157,255)(158,254)(159,253)(160,252)(161,275)(162,274)(163,273)(164,272)
(165,271)(166,270)(167,269)(168,268)(169,267)(170,266)(171,265)(172,264)
(173,263)(174,262)(175,261)(176,231)(177,235)(178,234)(179,233)(180,232)
(181,226)(182,230)(183,229)(184,228)(185,227)(186,250)(187,249)(188,248)
(189,247)(190,246)(191,245)(192,244)(193,243)(194,242)(195,241)(196,240)
(197,239)(198,238)(199,237)(200,236)(201,281)(202,285)(203,284)(204,283)
(205,282)(206,276)(207,280)(208,279)(209,278)(210,277)(211,300)(212,299)
(213,298)(214,297)(215,296)(216,295)(217,294)(218,293)(219,292)(220,291)
(221,290)(222,289)(223,288)(224,287)(225,286);;
s2 := ( 1,151)( 2,152)( 3,153)( 4,154)( 5,155)( 6,156)( 7,157)( 8,158)
( 9,159)( 10,160)( 11,161)( 12,162)( 13,163)( 14,164)( 15,165)( 16,166)
( 17,167)( 18,168)( 19,169)( 20,170)( 21,171)( 22,172)( 23,173)( 24,174)
( 25,175)( 26,176)( 27,177)( 28,178)( 29,179)( 30,180)( 31,181)( 32,182)
( 33,183)( 34,184)( 35,185)( 36,186)( 37,187)( 38,188)( 39,189)( 40,190)
( 41,191)( 42,192)( 43,193)( 44,194)( 45,195)( 46,196)( 47,197)( 48,198)
( 49,199)( 50,200)( 51,201)( 52,202)( 53,203)( 54,204)( 55,205)( 56,206)
( 57,207)( 58,208)( 59,209)( 60,210)( 61,211)( 62,212)( 63,213)( 64,214)
( 65,215)( 66,216)( 67,217)( 68,218)( 69,219)( 70,220)( 71,221)( 72,222)
( 73,223)( 74,224)( 75,225)( 76,226)( 77,227)( 78,228)( 79,229)( 80,230)
( 81,231)( 82,232)( 83,233)( 84,234)( 85,235)( 86,236)( 87,237)( 88,238)
( 89,239)( 90,240)( 91,241)( 92,242)( 93,243)( 94,244)( 95,245)( 96,246)
( 97,247)( 98,248)( 99,249)(100,250)(101,251)(102,252)(103,253)(104,254)
(105,255)(106,256)(107,257)(108,258)(109,259)(110,260)(111,261)(112,262)
(113,263)(114,264)(115,265)(116,266)(117,267)(118,268)(119,269)(120,270)
(121,271)(122,272)(123,273)(124,274)(125,275)(126,276)(127,277)(128,278)
(129,279)(130,280)(131,281)(132,282)(133,283)(134,284)(135,285)(136,286)
(137,287)(138,288)(139,289)(140,290)(141,291)(142,292)(143,293)(144,294)
(145,295)(146,296)(147,297)(148,298)(149,299)(150,300);;
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,
s1*s2*s1*s2*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*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*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(300)!( 2, 5)( 3, 4)( 6, 25)( 7, 24)( 8, 23)( 9, 22)( 10, 21)
( 11, 20)( 12, 19)( 13, 18)( 14, 17)( 15, 16)( 26, 51)( 27, 55)( 28, 54)
( 29, 53)( 30, 52)( 31, 75)( 32, 74)( 33, 73)( 34, 72)( 35, 71)( 36, 70)
( 37, 69)( 38, 68)( 39, 67)( 40, 66)( 41, 65)( 42, 64)( 43, 63)( 44, 62)
( 45, 61)( 46, 60)( 47, 59)( 48, 58)( 49, 57)( 50, 56)( 77, 80)( 78, 79)
( 81,100)( 82, 99)( 83, 98)( 84, 97)( 85, 96)( 86, 95)( 87, 94)( 88, 93)
( 89, 92)( 90, 91)(101,126)(102,130)(103,129)(104,128)(105,127)(106,150)
(107,149)(108,148)(109,147)(110,146)(111,145)(112,144)(113,143)(114,142)
(115,141)(116,140)(117,139)(118,138)(119,137)(120,136)(121,135)(122,134)
(123,133)(124,132)(125,131)(152,155)(153,154)(156,175)(157,174)(158,173)
(159,172)(160,171)(161,170)(162,169)(163,168)(164,167)(165,166)(176,201)
(177,205)(178,204)(179,203)(180,202)(181,225)(182,224)(183,223)(184,222)
(185,221)(186,220)(187,219)(188,218)(189,217)(190,216)(191,215)(192,214)
(193,213)(194,212)(195,211)(196,210)(197,209)(198,208)(199,207)(200,206)
(227,230)(228,229)(231,250)(232,249)(233,248)(234,247)(235,246)(236,245)
(237,244)(238,243)(239,242)(240,241)(251,276)(252,280)(253,279)(254,278)
(255,277)(256,300)(257,299)(258,298)(259,297)(260,296)(261,295)(262,294)
(263,293)(264,292)(265,291)(266,290)(267,289)(268,288)(269,287)(270,286)
(271,285)(272,284)(273,283)(274,282)(275,281);
s1 := Sym(300)!( 1, 31)( 2, 35)( 3, 34)( 4, 33)( 5, 32)( 6, 26)( 7, 30)
( 8, 29)( 9, 28)( 10, 27)( 11, 50)( 12, 49)( 13, 48)( 14, 47)( 15, 46)
( 16, 45)( 17, 44)( 18, 43)( 19, 42)( 20, 41)( 21, 40)( 22, 39)( 23, 38)
( 24, 37)( 25, 36)( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 61, 75)
( 62, 74)( 63, 73)( 64, 72)( 65, 71)( 66, 70)( 67, 69)( 76,106)( 77,110)
( 78,109)( 79,108)( 80,107)( 81,101)( 82,105)( 83,104)( 84,103)( 85,102)
( 86,125)( 87,124)( 88,123)( 89,122)( 90,121)( 91,120)( 92,119)( 93,118)
( 94,117)( 95,116)( 96,115)( 97,114)( 98,113)( 99,112)(100,111)(126,131)
(127,135)(128,134)(129,133)(130,132)(136,150)(137,149)(138,148)(139,147)
(140,146)(141,145)(142,144)(151,256)(152,260)(153,259)(154,258)(155,257)
(156,251)(157,255)(158,254)(159,253)(160,252)(161,275)(162,274)(163,273)
(164,272)(165,271)(166,270)(167,269)(168,268)(169,267)(170,266)(171,265)
(172,264)(173,263)(174,262)(175,261)(176,231)(177,235)(178,234)(179,233)
(180,232)(181,226)(182,230)(183,229)(184,228)(185,227)(186,250)(187,249)
(188,248)(189,247)(190,246)(191,245)(192,244)(193,243)(194,242)(195,241)
(196,240)(197,239)(198,238)(199,237)(200,236)(201,281)(202,285)(203,284)
(204,283)(205,282)(206,276)(207,280)(208,279)(209,278)(210,277)(211,300)
(212,299)(213,298)(214,297)(215,296)(216,295)(217,294)(218,293)(219,292)
(220,291)(221,290)(222,289)(223,288)(224,287)(225,286);
s2 := Sym(300)!( 1,151)( 2,152)( 3,153)( 4,154)( 5,155)( 6,156)( 7,157)
( 8,158)( 9,159)( 10,160)( 11,161)( 12,162)( 13,163)( 14,164)( 15,165)
( 16,166)( 17,167)( 18,168)( 19,169)( 20,170)( 21,171)( 22,172)( 23,173)
( 24,174)( 25,175)( 26,176)( 27,177)( 28,178)( 29,179)( 30,180)( 31,181)
( 32,182)( 33,183)( 34,184)( 35,185)( 36,186)( 37,187)( 38,188)( 39,189)
( 40,190)( 41,191)( 42,192)( 43,193)( 44,194)( 45,195)( 46,196)( 47,197)
( 48,198)( 49,199)( 50,200)( 51,201)( 52,202)( 53,203)( 54,204)( 55,205)
( 56,206)( 57,207)( 58,208)( 59,209)( 60,210)( 61,211)( 62,212)( 63,213)
( 64,214)( 65,215)( 66,216)( 67,217)( 68,218)( 69,219)( 70,220)( 71,221)
( 72,222)( 73,223)( 74,224)( 75,225)( 76,226)( 77,227)( 78,228)( 79,229)
( 80,230)( 81,231)( 82,232)( 83,233)( 84,234)( 85,235)( 86,236)( 87,237)
( 88,238)( 89,239)( 90,240)( 91,241)( 92,242)( 93,243)( 94,244)( 95,245)
( 96,246)( 97,247)( 98,248)( 99,249)(100,250)(101,251)(102,252)(103,253)
(104,254)(105,255)(106,256)(107,257)(108,258)(109,259)(110,260)(111,261)
(112,262)(113,263)(114,264)(115,265)(116,266)(117,267)(118,268)(119,269)
(120,270)(121,271)(122,272)(123,273)(124,274)(125,275)(126,276)(127,277)
(128,278)(129,279)(130,280)(131,281)(132,282)(133,283)(134,284)(135,285)
(136,286)(137,287)(138,288)(139,289)(140,290)(141,291)(142,292)(143,293)
(144,294)(145,295)(146,296)(147,297)(148,298)(149,299)(150,300);
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,
s1*s2*s1*s2*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*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*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