Polytope of Type {300,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {300,2}*1200
if this polytope has a name.
Group : SmallGroup(1200,171)
Rank : 3
Schlafli Type : {300,2}
Number of vertices, edges, etc : 300, 300, 2
Order of s₀s₁s₂ : 300
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
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 : {100,2}*400
   4-fold quotients : {75,2}*300
   5-fold quotients : {60,2}*240
   6-fold quotients : {50,2}*200
   10-fold quotients : {30,2}*120
   12-fold quotients : {25,2}*100
   15-fold quotients : {20,2}*80
   20-fold quotients : {15,2}*60
   25-fold quotients : {12,2}*48
   30-fold quotients : {10,2}*40
   50-fold quotients : {6,2}*24
   60-fold quotients : {5,2}*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 := (  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)(151,226)(152,230)(153,229)(154,228)(155,227)(156,250)
(157,249)(158,248)(159,247)(160,246)(161,245)(162,244)(163,243)(164,242)
(165,241)(166,240)(167,239)(168,238)(169,237)(170,236)(171,235)(172,234)
(173,233)(174,232)(175,231)(176,276)(177,280)(178,279)(179,278)(180,277)
(181,300)(182,299)(183,298)(184,297)(185,296)(186,295)(187,294)(188,293)
(189,292)(190,291)(191,290)(192,289)(193,288)(194,287)(195,286)(196,285)
(197,284)(198,283)(199,282)(200,281)(201,251)(202,255)(203,254)(204,253)
(205,252)(206,275)(207,274)(208,273)(209,272)(210,271)(211,270)(212,269)
(213,268)(214,267)(215,266)(216,265)(217,264)(218,263)(219,262)(220,261)
(221,260)(222,259)(223,258)(224,257)(225,256);;
s1 := (  1,181)(  2,185)(  3,184)(  4,183)(  5,182)(  6,176)(  7,180)(  8,179)
(  9,178)( 10,177)( 11,200)( 12,199)( 13,198)( 14,197)( 15,196)( 16,195)
( 17,194)( 18,193)( 19,192)( 20,191)( 21,190)( 22,189)( 23,188)( 24,187)
( 25,186)( 26,156)( 27,160)( 28,159)( 29,158)( 30,157)( 31,151)( 32,155)
( 33,154)( 34,153)( 35,152)( 36,175)( 37,174)( 38,173)( 39,172)( 40,171)
( 41,170)( 42,169)( 43,168)( 44,167)( 45,166)( 46,165)( 47,164)( 48,163)
( 49,162)( 50,161)( 51,206)( 52,210)( 53,209)( 54,208)( 55,207)( 56,201)
( 57,205)( 58,204)( 59,203)( 60,202)( 61,225)( 62,224)( 63,223)( 64,222)
( 65,221)( 66,220)( 67,219)( 68,218)( 69,217)( 70,216)( 71,215)( 72,214)
( 73,213)( 74,212)( 75,211)( 76,256)( 77,260)( 78,259)( 79,258)( 80,257)
( 81,251)( 82,255)( 83,254)( 84,253)( 85,252)( 86,275)( 87,274)( 88,273)
( 89,272)( 90,271)( 91,270)( 92,269)( 93,268)( 94,267)( 95,266)( 96,265)
( 97,264)( 98,263)( 99,262)(100,261)(101,231)(102,235)(103,234)(104,233)
(105,232)(106,226)(107,230)(108,229)(109,228)(110,227)(111,250)(112,249)
(113,248)(114,247)(115,246)(116,245)(117,244)(118,243)(119,242)(120,241)
(121,240)(122,239)(123,238)(124,237)(125,236)(126,281)(127,285)(128,284)
(129,283)(130,282)(131,276)(132,280)(133,279)(134,278)(135,277)(136,300)
(137,299)(138,298)(139,297)(140,296)(141,295)(142,294)(143,293)(144,292)
(145,291)(146,290)(147,289)(148,288)(149,287)(150,286);;
s2 := (301,302);;
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, 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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(302)!(  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)(151,226)(152,230)(153,229)(154,228)(155,227)
(156,250)(157,249)(158,248)(159,247)(160,246)(161,245)(162,244)(163,243)
(164,242)(165,241)(166,240)(167,239)(168,238)(169,237)(170,236)(171,235)
(172,234)(173,233)(174,232)(175,231)(176,276)(177,280)(178,279)(179,278)
(180,277)(181,300)(182,299)(183,298)(184,297)(185,296)(186,295)(187,294)
(188,293)(189,292)(190,291)(191,290)(192,289)(193,288)(194,287)(195,286)
(196,285)(197,284)(198,283)(199,282)(200,281)(201,251)(202,255)(203,254)
(204,253)(205,252)(206,275)(207,274)(208,273)(209,272)(210,271)(211,270)
(212,269)(213,268)(214,267)(215,266)(216,265)(217,264)(218,263)(219,262)
(220,261)(221,260)(222,259)(223,258)(224,257)(225,256);
s1 := Sym(302)!(  1,181)(  2,185)(  3,184)(  4,183)(  5,182)(  6,176)(  7,180)
(  8,179)(  9,178)( 10,177)( 11,200)( 12,199)( 13,198)( 14,197)( 15,196)
( 16,195)( 17,194)( 18,193)( 19,192)( 20,191)( 21,190)( 22,189)( 23,188)
( 24,187)( 25,186)( 26,156)( 27,160)( 28,159)( 29,158)( 30,157)( 31,151)
( 32,155)( 33,154)( 34,153)( 35,152)( 36,175)( 37,174)( 38,173)( 39,172)
( 40,171)( 41,170)( 42,169)( 43,168)( 44,167)( 45,166)( 46,165)( 47,164)
( 48,163)( 49,162)( 50,161)( 51,206)( 52,210)( 53,209)( 54,208)( 55,207)
( 56,201)( 57,205)( 58,204)( 59,203)( 60,202)( 61,225)( 62,224)( 63,223)
( 64,222)( 65,221)( 66,220)( 67,219)( 68,218)( 69,217)( 70,216)( 71,215)
( 72,214)( 73,213)( 74,212)( 75,211)( 76,256)( 77,260)( 78,259)( 79,258)
( 80,257)( 81,251)( 82,255)( 83,254)( 84,253)( 85,252)( 86,275)( 87,274)
( 88,273)( 89,272)( 90,271)( 91,270)( 92,269)( 93,268)( 94,267)( 95,266)
( 96,265)( 97,264)( 98,263)( 99,262)(100,261)(101,231)(102,235)(103,234)
(104,233)(105,232)(106,226)(107,230)(108,229)(109,228)(110,227)(111,250)
(112,249)(113,248)(114,247)(115,246)(116,245)(117,244)(118,243)(119,242)
(120,241)(121,240)(122,239)(123,238)(124,237)(125,236)(126,281)(127,285)
(128,284)(129,283)(130,282)(131,276)(132,280)(133,279)(134,278)(135,277)
(136,300)(137,299)(138,298)(139,297)(140,296)(141,295)(142,294)(143,293)
(144,292)(145,291)(146,290)(147,289)(148,288)(149,287)(150,286);
s2 := Sym(302)!(301,302);
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*s2*s0*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope