Polytope of Type {219,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {219,4}*1752
if this polytope has a name.
Group : SmallGroup(1752,51)
Rank : 3
Schlafli Type : {219,4}
Number of vertices, edges, etc : 219, 438, 4
Order of s0s1s2 : 219
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Flat
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
73-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5,289)( 6,290)( 7,292)( 8,291)( 9,285)( 10,286)( 11,288)
( 12,287)( 13,281)( 14,282)( 15,284)( 16,283)( 17,277)( 18,278)( 19,280)
( 20,279)( 21,273)( 22,274)( 23,276)( 24,275)( 25,269)( 26,270)( 27,272)
( 28,271)( 29,265)( 30,266)( 31,268)( 32,267)( 33,261)( 34,262)( 35,264)
( 36,263)( 37,257)( 38,258)( 39,260)( 40,259)( 41,253)( 42,254)( 43,256)
( 44,255)( 45,249)( 46,250)( 47,252)( 48,251)( 49,245)( 50,246)( 51,248)
( 52,247)( 53,241)( 54,242)( 55,244)( 56,243)( 57,237)( 58,238)( 59,240)
( 60,239)( 61,233)( 62,234)( 63,236)( 64,235)( 65,229)( 66,230)( 67,232)
( 68,231)( 69,225)( 70,226)( 71,228)( 72,227)( 73,221)( 74,222)( 75,224)
( 76,223)( 77,217)( 78,218)( 79,220)( 80,219)( 81,213)( 82,214)( 83,216)
( 84,215)( 85,209)( 86,210)( 87,212)( 88,211)( 89,205)( 90,206)( 91,208)
( 92,207)( 93,201)( 94,202)( 95,204)( 96,203)( 97,197)( 98,198)( 99,200)
(100,199)(101,193)(102,194)(103,196)(104,195)(105,189)(106,190)(107,192)
(108,191)(109,185)(110,186)(111,188)(112,187)(113,181)(114,182)(115,184)
(116,183)(117,177)(118,178)(119,180)(120,179)(121,173)(122,174)(123,176)
(124,175)(125,169)(126,170)(127,172)(128,171)(129,165)(130,166)(131,168)
(132,167)(133,161)(134,162)(135,164)(136,163)(137,157)(138,158)(139,160)
(140,159)(141,153)(142,154)(143,156)(144,155)(145,149)(146,150)(147,152)
(148,151);;
s1 := ( 1, 5)( 2, 8)( 3, 7)( 4, 6)( 9,289)( 10,292)( 11,291)( 12,290)
( 13,285)( 14,288)( 15,287)( 16,286)( 17,281)( 18,284)( 19,283)( 20,282)
( 21,277)( 22,280)( 23,279)( 24,278)( 25,273)( 26,276)( 27,275)( 28,274)
( 29,269)( 30,272)( 31,271)( 32,270)( 33,265)( 34,268)( 35,267)( 36,266)
( 37,261)( 38,264)( 39,263)( 40,262)( 41,257)( 42,260)( 43,259)( 44,258)
( 45,253)( 46,256)( 47,255)( 48,254)( 49,249)( 50,252)( 51,251)( 52,250)
( 53,245)( 54,248)( 55,247)( 56,246)( 57,241)( 58,244)( 59,243)( 60,242)
( 61,237)( 62,240)( 63,239)( 64,238)( 65,233)( 66,236)( 67,235)( 68,234)
( 69,229)( 70,232)( 71,231)( 72,230)( 73,225)( 74,228)( 75,227)( 76,226)
( 77,221)( 78,224)( 79,223)( 80,222)( 81,217)( 82,220)( 83,219)( 84,218)
( 85,213)( 86,216)( 87,215)( 88,214)( 89,209)( 90,212)( 91,211)( 92,210)
( 93,205)( 94,208)( 95,207)( 96,206)( 97,201)( 98,204)( 99,203)(100,202)
(101,197)(102,200)(103,199)(104,198)(105,193)(106,196)(107,195)(108,194)
(109,189)(110,192)(111,191)(112,190)(113,185)(114,188)(115,187)(116,186)
(117,181)(118,184)(119,183)(120,182)(121,177)(122,180)(123,179)(124,178)
(125,173)(126,176)(127,175)(128,174)(129,169)(130,172)(131,171)(132,170)
(133,165)(134,168)(135,167)(136,166)(137,161)(138,164)(139,163)(140,162)
(141,157)(142,160)(143,159)(144,158)(145,153)(146,156)(147,155)(148,154)
(150,152);;
s2 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)( 15, 16)
( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)
( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)
( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)
( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)
( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)
( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)
(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)
(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)
(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)
(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)
(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)
(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(207,208)
(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)(223,224)
(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)(239,240)
(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)(255,256)
(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)(271,272)
(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)(287,288)
(289,290)(291,292);;
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*s1*s2*s1*s2,
s2*s1*s0*s2*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(292)!( 3, 4)( 5,289)( 6,290)( 7,292)( 8,291)( 9,285)( 10,286)
( 11,288)( 12,287)( 13,281)( 14,282)( 15,284)( 16,283)( 17,277)( 18,278)
( 19,280)( 20,279)( 21,273)( 22,274)( 23,276)( 24,275)( 25,269)( 26,270)
( 27,272)( 28,271)( 29,265)( 30,266)( 31,268)( 32,267)( 33,261)( 34,262)
( 35,264)( 36,263)( 37,257)( 38,258)( 39,260)( 40,259)( 41,253)( 42,254)
( 43,256)( 44,255)( 45,249)( 46,250)( 47,252)( 48,251)( 49,245)( 50,246)
( 51,248)( 52,247)( 53,241)( 54,242)( 55,244)( 56,243)( 57,237)( 58,238)
( 59,240)( 60,239)( 61,233)( 62,234)( 63,236)( 64,235)( 65,229)( 66,230)
( 67,232)( 68,231)( 69,225)( 70,226)( 71,228)( 72,227)( 73,221)( 74,222)
( 75,224)( 76,223)( 77,217)( 78,218)( 79,220)( 80,219)( 81,213)( 82,214)
( 83,216)( 84,215)( 85,209)( 86,210)( 87,212)( 88,211)( 89,205)( 90,206)
( 91,208)( 92,207)( 93,201)( 94,202)( 95,204)( 96,203)( 97,197)( 98,198)
( 99,200)(100,199)(101,193)(102,194)(103,196)(104,195)(105,189)(106,190)
(107,192)(108,191)(109,185)(110,186)(111,188)(112,187)(113,181)(114,182)
(115,184)(116,183)(117,177)(118,178)(119,180)(120,179)(121,173)(122,174)
(123,176)(124,175)(125,169)(126,170)(127,172)(128,171)(129,165)(130,166)
(131,168)(132,167)(133,161)(134,162)(135,164)(136,163)(137,157)(138,158)
(139,160)(140,159)(141,153)(142,154)(143,156)(144,155)(145,149)(146,150)
(147,152)(148,151);
s1 := Sym(292)!( 1, 5)( 2, 8)( 3, 7)( 4, 6)( 9,289)( 10,292)( 11,291)
( 12,290)( 13,285)( 14,288)( 15,287)( 16,286)( 17,281)( 18,284)( 19,283)
( 20,282)( 21,277)( 22,280)( 23,279)( 24,278)( 25,273)( 26,276)( 27,275)
( 28,274)( 29,269)( 30,272)( 31,271)( 32,270)( 33,265)( 34,268)( 35,267)
( 36,266)( 37,261)( 38,264)( 39,263)( 40,262)( 41,257)( 42,260)( 43,259)
( 44,258)( 45,253)( 46,256)( 47,255)( 48,254)( 49,249)( 50,252)( 51,251)
( 52,250)( 53,245)( 54,248)( 55,247)( 56,246)( 57,241)( 58,244)( 59,243)
( 60,242)( 61,237)( 62,240)( 63,239)( 64,238)( 65,233)( 66,236)( 67,235)
( 68,234)( 69,229)( 70,232)( 71,231)( 72,230)( 73,225)( 74,228)( 75,227)
( 76,226)( 77,221)( 78,224)( 79,223)( 80,222)( 81,217)( 82,220)( 83,219)
( 84,218)( 85,213)( 86,216)( 87,215)( 88,214)( 89,209)( 90,212)( 91,211)
( 92,210)( 93,205)( 94,208)( 95,207)( 96,206)( 97,201)( 98,204)( 99,203)
(100,202)(101,197)(102,200)(103,199)(104,198)(105,193)(106,196)(107,195)
(108,194)(109,189)(110,192)(111,191)(112,190)(113,185)(114,188)(115,187)
(116,186)(117,181)(118,184)(119,183)(120,182)(121,177)(122,180)(123,179)
(124,178)(125,173)(126,176)(127,175)(128,174)(129,169)(130,172)(131,171)
(132,170)(133,165)(134,168)(135,167)(136,166)(137,161)(138,164)(139,163)
(140,162)(141,157)(142,160)(143,159)(144,158)(145,153)(146,156)(147,155)
(148,154)(150,152);
s2 := Sym(292)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)
( 15, 16)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)
( 31, 32)( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)
( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)
( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)
( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)
( 95, 96)( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)
(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)
(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)
(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)
(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)
(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)
(191,192)(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)
(207,208)(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)
(223,224)(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)
(239,240)(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)
(255,256)(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)
(271,272)(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)
(287,288)(289,290)(291,292);
poly := sub<Sym(292)|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*s1*s2*s1*s2,
s2*s1*s0*s2*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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