Polytope of Type {2,300}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,300}*1200
if this polytope has a name.
Group : SmallGroup(1200,171)
Rank : 3
Schlafli Type : {2,300}
Number of vertices, edges, etc : 2, 300, 300
Order of s0s1s2 : 300
Order of s0s1s2s1 : 2
Special Properties :
Degenerate
Universal
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 : {2,150}*600
3-fold quotients : {2,100}*400
4-fold quotients : {2,75}*300
5-fold quotients : {2,60}*240
6-fold quotients : {2,50}*200
10-fold quotients : {2,30}*120
12-fold quotients : {2,25}*100
15-fold quotients : {2,20}*80
20-fold quotients : {2,15}*60
25-fold quotients : {2,12}*48
30-fold quotients : {2,10}*40
50-fold quotients : {2,6}*24
60-fold quotients : {2,5}*20
75-fold quotients : {2,4}*16
100-fold quotients : {2,3}*12
150-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 7)( 5, 6)( 8, 27)( 9, 26)( 10, 25)( 11, 24)( 12, 23)( 13, 22)
( 14, 21)( 15, 20)( 16, 19)( 17, 18)( 28, 53)( 29, 57)( 30, 56)( 31, 55)
( 32, 54)( 33, 77)( 34, 76)( 35, 75)( 36, 74)( 37, 73)( 38, 72)( 39, 71)
( 40, 70)( 41, 69)( 42, 68)( 43, 67)( 44, 66)( 45, 65)( 46, 64)( 47, 63)
( 48, 62)( 49, 61)( 50, 60)( 51, 59)( 52, 58)( 79, 82)( 80, 81)( 83,102)
( 84,101)( 85,100)( 86, 99)( 87, 98)( 88, 97)( 89, 96)( 90, 95)( 91, 94)
( 92, 93)(103,128)(104,132)(105,131)(106,130)(107,129)(108,152)(109,151)
(110,150)(111,149)(112,148)(113,147)(114,146)(115,145)(116,144)(117,143)
(118,142)(119,141)(120,140)(121,139)(122,138)(123,137)(124,136)(125,135)
(126,134)(127,133)(153,228)(154,232)(155,231)(156,230)(157,229)(158,252)
(159,251)(160,250)(161,249)(162,248)(163,247)(164,246)(165,245)(166,244)
(167,243)(168,242)(169,241)(170,240)(171,239)(172,238)(173,237)(174,236)
(175,235)(176,234)(177,233)(178,278)(179,282)(180,281)(181,280)(182,279)
(183,302)(184,301)(185,300)(186,299)(187,298)(188,297)(189,296)(190,295)
(191,294)(192,293)(193,292)(194,291)(195,290)(196,289)(197,288)(198,287)
(199,286)(200,285)(201,284)(202,283)(203,253)(204,257)(205,256)(206,255)
(207,254)(208,277)(209,276)(210,275)(211,274)(212,273)(213,272)(214,271)
(215,270)(216,269)(217,268)(218,267)(219,266)(220,265)(221,264)(222,263)
(223,262)(224,261)(225,260)(226,259)(227,258);;
s2 := ( 3,183)( 4,187)( 5,186)( 6,185)( 7,184)( 8,178)( 9,182)( 10,181)
( 11,180)( 12,179)( 13,202)( 14,201)( 15,200)( 16,199)( 17,198)( 18,197)
( 19,196)( 20,195)( 21,194)( 22,193)( 23,192)( 24,191)( 25,190)( 26,189)
( 27,188)( 28,158)( 29,162)( 30,161)( 31,160)( 32,159)( 33,153)( 34,157)
( 35,156)( 36,155)( 37,154)( 38,177)( 39,176)( 40,175)( 41,174)( 42,173)
( 43,172)( 44,171)( 45,170)( 46,169)( 47,168)( 48,167)( 49,166)( 50,165)
( 51,164)( 52,163)( 53,208)( 54,212)( 55,211)( 56,210)( 57,209)( 58,203)
( 59,207)( 60,206)( 61,205)( 62,204)( 63,227)( 64,226)( 65,225)( 66,224)
( 67,223)( 68,222)( 69,221)( 70,220)( 71,219)( 72,218)( 73,217)( 74,216)
( 75,215)( 76,214)( 77,213)( 78,258)( 79,262)( 80,261)( 81,260)( 82,259)
( 83,253)( 84,257)( 85,256)( 86,255)( 87,254)( 88,277)( 89,276)( 90,275)
( 91,274)( 92,273)( 93,272)( 94,271)( 95,270)( 96,269)( 97,268)( 98,267)
( 99,266)(100,265)(101,264)(102,263)(103,233)(104,237)(105,236)(106,235)
(107,234)(108,228)(109,232)(110,231)(111,230)(112,229)(113,252)(114,251)
(115,250)(116,249)(117,248)(118,247)(119,246)(120,245)(121,244)(122,243)
(123,242)(124,241)(125,240)(126,239)(127,238)(128,283)(129,287)(130,286)
(131,285)(132,284)(133,278)(134,282)(135,281)(136,280)(137,279)(138,302)
(139,301)(140,300)(141,299)(142,298)(143,297)(144,296)(145,295)(146,294)
(147,293)(148,292)(149,291)(150,290)(151,289)(152,288);;
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*s1*s0*s1, s0*s2*s0*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*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*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*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*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*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*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(302)!(1,2);
s1 := Sym(302)!( 4, 7)( 5, 6)( 8, 27)( 9, 26)( 10, 25)( 11, 24)( 12, 23)
( 13, 22)( 14, 21)( 15, 20)( 16, 19)( 17, 18)( 28, 53)( 29, 57)( 30, 56)
( 31, 55)( 32, 54)( 33, 77)( 34, 76)( 35, 75)( 36, 74)( 37, 73)( 38, 72)
( 39, 71)( 40, 70)( 41, 69)( 42, 68)( 43, 67)( 44, 66)( 45, 65)( 46, 64)
( 47, 63)( 48, 62)( 49, 61)( 50, 60)( 51, 59)( 52, 58)( 79, 82)( 80, 81)
( 83,102)( 84,101)( 85,100)( 86, 99)( 87, 98)( 88, 97)( 89, 96)( 90, 95)
( 91, 94)( 92, 93)(103,128)(104,132)(105,131)(106,130)(107,129)(108,152)
(109,151)(110,150)(111,149)(112,148)(113,147)(114,146)(115,145)(116,144)
(117,143)(118,142)(119,141)(120,140)(121,139)(122,138)(123,137)(124,136)
(125,135)(126,134)(127,133)(153,228)(154,232)(155,231)(156,230)(157,229)
(158,252)(159,251)(160,250)(161,249)(162,248)(163,247)(164,246)(165,245)
(166,244)(167,243)(168,242)(169,241)(170,240)(171,239)(172,238)(173,237)
(174,236)(175,235)(176,234)(177,233)(178,278)(179,282)(180,281)(181,280)
(182,279)(183,302)(184,301)(185,300)(186,299)(187,298)(188,297)(189,296)
(190,295)(191,294)(192,293)(193,292)(194,291)(195,290)(196,289)(197,288)
(198,287)(199,286)(200,285)(201,284)(202,283)(203,253)(204,257)(205,256)
(206,255)(207,254)(208,277)(209,276)(210,275)(211,274)(212,273)(213,272)
(214,271)(215,270)(216,269)(217,268)(218,267)(219,266)(220,265)(221,264)
(222,263)(223,262)(224,261)(225,260)(226,259)(227,258);
s2 := Sym(302)!( 3,183)( 4,187)( 5,186)( 6,185)( 7,184)( 8,178)( 9,182)
( 10,181)( 11,180)( 12,179)( 13,202)( 14,201)( 15,200)( 16,199)( 17,198)
( 18,197)( 19,196)( 20,195)( 21,194)( 22,193)( 23,192)( 24,191)( 25,190)
( 26,189)( 27,188)( 28,158)( 29,162)( 30,161)( 31,160)( 32,159)( 33,153)
( 34,157)( 35,156)( 36,155)( 37,154)( 38,177)( 39,176)( 40,175)( 41,174)
( 42,173)( 43,172)( 44,171)( 45,170)( 46,169)( 47,168)( 48,167)( 49,166)
( 50,165)( 51,164)( 52,163)( 53,208)( 54,212)( 55,211)( 56,210)( 57,209)
( 58,203)( 59,207)( 60,206)( 61,205)( 62,204)( 63,227)( 64,226)( 65,225)
( 66,224)( 67,223)( 68,222)( 69,221)( 70,220)( 71,219)( 72,218)( 73,217)
( 74,216)( 75,215)( 76,214)( 77,213)( 78,258)( 79,262)( 80,261)( 81,260)
( 82,259)( 83,253)( 84,257)( 85,256)( 86,255)( 87,254)( 88,277)( 89,276)
( 90,275)( 91,274)( 92,273)( 93,272)( 94,271)( 95,270)( 96,269)( 97,268)
( 98,267)( 99,266)(100,265)(101,264)(102,263)(103,233)(104,237)(105,236)
(106,235)(107,234)(108,228)(109,232)(110,231)(111,230)(112,229)(113,252)
(114,251)(115,250)(116,249)(117,248)(118,247)(119,246)(120,245)(121,244)
(122,243)(123,242)(124,241)(125,240)(126,239)(127,238)(128,283)(129,287)
(130,286)(131,285)(132,284)(133,278)(134,282)(135,281)(136,280)(137,279)
(138,302)(139,301)(140,300)(141,299)(142,298)(143,297)(144,296)(145,295)
(146,294)(147,293)(148,292)(149,291)(150,290)(151,289)(152,288);
poly := sub<Sym(302)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s1*s0*s1, s0*s2*s0*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*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*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*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*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*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*s1*s2 >;
to this polytope