Polytope of Type {4,249}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,249}*1992
if this polytope has a name.
Group : SmallGroup(1992,32)
Rank : 3
Schlafli Type : {4,249}
Number of vertices, edges, etc : 4, 498, 249
Order of s₀s₁s₂ : 249
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-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) :
   83-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  1,  3)(  2,  4)(  5,  7)(  6,  8)(  9, 11)( 10, 12)( 13, 15)( 14, 16)
( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)
( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)
( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)
( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)
( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)
( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)
(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)(126,128)
(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)(142,144)
(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)(158,160)
(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)(174,176)
(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)(190,192)
(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)(206,208)
(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)(222,224)
(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)(238,240)
(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)(254,256)
(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)(270,272)
(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)(286,288)
(289,291)(290,292)(293,295)(294,296)(297,299)(298,300)(301,303)(302,304)
(305,307)(306,308)(309,311)(310,312)(313,315)(314,316)(317,319)(318,320)
(321,323)(322,324)(325,327)(326,328)(329,331)(330,332);;
s1 := (  3,  4)(  5,329)(  6,330)(  7,332)(  8,331)(  9,325)( 10,326)( 11,328)
( 12,327)( 13,321)( 14,322)( 15,324)( 16,323)( 17,317)( 18,318)( 19,320)
( 20,319)( 21,313)( 22,314)( 23,316)( 24,315)( 25,309)( 26,310)( 27,312)
( 28,311)( 29,305)( 30,306)( 31,308)( 32,307)( 33,301)( 34,302)( 35,304)
( 36,303)( 37,297)( 38,298)( 39,300)( 40,299)( 41,293)( 42,294)( 43,296)
( 44,295)( 45,289)( 46,290)( 47,292)( 48,291)( 49,285)( 50,286)( 51,288)
( 52,287)( 53,281)( 54,282)( 55,284)( 56,283)( 57,277)( 58,278)( 59,280)
( 60,279)( 61,273)( 62,274)( 63,276)( 64,275)( 65,269)( 66,270)( 67,272)
( 68,271)( 69,265)( 70,266)( 71,268)( 72,267)( 73,261)( 74,262)( 75,264)
( 76,263)( 77,257)( 78,258)( 79,260)( 80,259)( 81,253)( 82,254)( 83,256)
( 84,255)( 85,249)( 86,250)( 87,252)( 88,251)( 89,245)( 90,246)( 91,248)
( 92,247)( 93,241)( 94,242)( 95,244)( 96,243)( 97,237)( 98,238)( 99,240)
(100,239)(101,233)(102,234)(103,236)(104,235)(105,229)(106,230)(107,232)
(108,231)(109,225)(110,226)(111,228)(112,227)(113,221)(114,222)(115,224)
(116,223)(117,217)(118,218)(119,220)(120,219)(121,213)(122,214)(123,216)
(124,215)(125,209)(126,210)(127,212)(128,211)(129,205)(130,206)(131,208)
(132,207)(133,201)(134,202)(135,204)(136,203)(137,197)(138,198)(139,200)
(140,199)(141,193)(142,194)(143,196)(144,195)(145,189)(146,190)(147,192)
(148,191)(149,185)(150,186)(151,188)(152,187)(153,181)(154,182)(155,184)
(156,183)(157,177)(158,178)(159,180)(160,179)(161,173)(162,174)(163,176)
(164,175)(165,169)(166,170)(167,172)(168,171);;
s2 := (  1,  5)(  2,  8)(  3,  7)(  4,  6)(  9,329)( 10,332)( 11,331)( 12,330)
( 13,325)( 14,328)( 15,327)( 16,326)( 17,321)( 18,324)( 19,323)( 20,322)
( 21,317)( 22,320)( 23,319)( 24,318)( 25,313)( 26,316)( 27,315)( 28,314)
( 29,309)( 30,312)( 31,311)( 32,310)( 33,305)( 34,308)( 35,307)( 36,306)
( 37,301)( 38,304)( 39,303)( 40,302)( 41,297)( 42,300)( 43,299)( 44,298)
( 45,293)( 46,296)( 47,295)( 48,294)( 49,289)( 50,292)( 51,291)( 52,290)
( 53,285)( 54,288)( 55,287)( 56,286)( 57,281)( 58,284)( 59,283)( 60,282)
( 61,277)( 62,280)( 63,279)( 64,278)( 65,273)( 66,276)( 67,275)( 68,274)
( 69,269)( 70,272)( 71,271)( 72,270)( 73,265)( 74,268)( 75,267)( 76,266)
( 77,261)( 78,264)( 79,263)( 80,262)( 81,257)( 82,260)( 83,259)( 84,258)
( 85,253)( 86,256)( 87,255)( 88,254)( 89,249)( 90,252)( 91,251)( 92,250)
( 93,245)( 94,248)( 95,247)( 96,246)( 97,241)( 98,244)( 99,243)(100,242)
(101,237)(102,240)(103,239)(104,238)(105,233)(106,236)(107,235)(108,234)
(109,229)(110,232)(111,231)(112,230)(113,225)(114,228)(115,227)(116,226)
(117,221)(118,224)(119,223)(120,222)(121,217)(122,220)(123,219)(124,218)
(125,213)(126,216)(127,215)(128,214)(129,209)(130,212)(131,211)(132,210)
(133,205)(134,208)(135,207)(136,206)(137,201)(138,204)(139,203)(140,202)
(141,197)(142,200)(143,199)(144,198)(145,193)(146,196)(147,195)(148,194)
(149,189)(150,192)(151,191)(152,190)(153,185)(154,188)(155,187)(156,186)
(157,181)(158,184)(159,183)(160,182)(161,177)(162,180)(163,179)(164,178)
(165,173)(166,176)(167,175)(168,174)(170,172);;
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*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(332)!(  1,  3)(  2,  4)(  5,  7)(  6,  8)(  9, 11)( 10, 12)( 13, 15)
( 14, 16)( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)
( 30, 32)( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)
( 46, 48)( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)
( 62, 64)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)
( 78, 80)( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)
( 94, 96)( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)
(110,112)(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)
(126,128)(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)
(142,144)(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)
(158,160)(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)
(174,176)(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)
(190,192)(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)
(206,208)(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)
(222,224)(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)
(238,240)(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)
(254,256)(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)
(270,272)(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)
(286,288)(289,291)(290,292)(293,295)(294,296)(297,299)(298,300)(301,303)
(302,304)(305,307)(306,308)(309,311)(310,312)(313,315)(314,316)(317,319)
(318,320)(321,323)(322,324)(325,327)(326,328)(329,331)(330,332);
s1 := Sym(332)!(  3,  4)(  5,329)(  6,330)(  7,332)(  8,331)(  9,325)( 10,326)
( 11,328)( 12,327)( 13,321)( 14,322)( 15,324)( 16,323)( 17,317)( 18,318)
( 19,320)( 20,319)( 21,313)( 22,314)( 23,316)( 24,315)( 25,309)( 26,310)
( 27,312)( 28,311)( 29,305)( 30,306)( 31,308)( 32,307)( 33,301)( 34,302)
( 35,304)( 36,303)( 37,297)( 38,298)( 39,300)( 40,299)( 41,293)( 42,294)
( 43,296)( 44,295)( 45,289)( 46,290)( 47,292)( 48,291)( 49,285)( 50,286)
( 51,288)( 52,287)( 53,281)( 54,282)( 55,284)( 56,283)( 57,277)( 58,278)
( 59,280)( 60,279)( 61,273)( 62,274)( 63,276)( 64,275)( 65,269)( 66,270)
( 67,272)( 68,271)( 69,265)( 70,266)( 71,268)( 72,267)( 73,261)( 74,262)
( 75,264)( 76,263)( 77,257)( 78,258)( 79,260)( 80,259)( 81,253)( 82,254)
( 83,256)( 84,255)( 85,249)( 86,250)( 87,252)( 88,251)( 89,245)( 90,246)
( 91,248)( 92,247)( 93,241)( 94,242)( 95,244)( 96,243)( 97,237)( 98,238)
( 99,240)(100,239)(101,233)(102,234)(103,236)(104,235)(105,229)(106,230)
(107,232)(108,231)(109,225)(110,226)(111,228)(112,227)(113,221)(114,222)
(115,224)(116,223)(117,217)(118,218)(119,220)(120,219)(121,213)(122,214)
(123,216)(124,215)(125,209)(126,210)(127,212)(128,211)(129,205)(130,206)
(131,208)(132,207)(133,201)(134,202)(135,204)(136,203)(137,197)(138,198)
(139,200)(140,199)(141,193)(142,194)(143,196)(144,195)(145,189)(146,190)
(147,192)(148,191)(149,185)(150,186)(151,188)(152,187)(153,181)(154,182)
(155,184)(156,183)(157,177)(158,178)(159,180)(160,179)(161,173)(162,174)
(163,176)(164,175)(165,169)(166,170)(167,172)(168,171);
s2 := Sym(332)!(  1,  5)(  2,  8)(  3,  7)(  4,  6)(  9,329)( 10,332)( 11,331)
( 12,330)( 13,325)( 14,328)( 15,327)( 16,326)( 17,321)( 18,324)( 19,323)
( 20,322)( 21,317)( 22,320)( 23,319)( 24,318)( 25,313)( 26,316)( 27,315)
( 28,314)( 29,309)( 30,312)( 31,311)( 32,310)( 33,305)( 34,308)( 35,307)
( 36,306)( 37,301)( 38,304)( 39,303)( 40,302)( 41,297)( 42,300)( 43,299)
( 44,298)( 45,293)( 46,296)( 47,295)( 48,294)( 49,289)( 50,292)( 51,291)
( 52,290)( 53,285)( 54,288)( 55,287)( 56,286)( 57,281)( 58,284)( 59,283)
( 60,282)( 61,277)( 62,280)( 63,279)( 64,278)( 65,273)( 66,276)( 67,275)
( 68,274)( 69,269)( 70,272)( 71,271)( 72,270)( 73,265)( 74,268)( 75,267)
( 76,266)( 77,261)( 78,264)( 79,263)( 80,262)( 81,257)( 82,260)( 83,259)
( 84,258)( 85,253)( 86,256)( 87,255)( 88,254)( 89,249)( 90,252)( 91,251)
( 92,250)( 93,245)( 94,248)( 95,247)( 96,246)( 97,241)( 98,244)( 99,243)
(100,242)(101,237)(102,240)(103,239)(104,238)(105,233)(106,236)(107,235)
(108,234)(109,229)(110,232)(111,231)(112,230)(113,225)(114,228)(115,227)
(116,226)(117,221)(118,224)(119,223)(120,222)(121,217)(122,220)(123,219)
(124,218)(125,213)(126,216)(127,215)(128,214)(129,209)(130,212)(131,211)
(132,210)(133,205)(134,208)(135,207)(136,206)(137,201)(138,204)(139,203)
(140,202)(141,197)(142,200)(143,199)(144,198)(145,193)(146,196)(147,195)
(148,194)(149,189)(150,192)(151,191)(152,190)(153,185)(154,188)(155,187)
(156,186)(157,181)(158,184)(159,183)(160,182)(161,177)(162,180)(163,179)
(164,178)(165,173)(166,176)(167,175)(168,174)(170,172);
poly := sub<Sym(332)|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*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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