Polytope of Type {213,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {213,4}*1704
if this polytope has a name.
Group : SmallGroup(1704,32)
Rank : 3
Schlafli Type : {213,4}
Number of vertices, edges, etc : 213, 426, 4
Order of s0s1s2 : 213
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) :
71-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5,281)( 6,282)( 7,284)( 8,283)( 9,277)( 10,278)( 11,280)
( 12,279)( 13,273)( 14,274)( 15,276)( 16,275)( 17,269)( 18,270)( 19,272)
( 20,271)( 21,265)( 22,266)( 23,268)( 24,267)( 25,261)( 26,262)( 27,264)
( 28,263)( 29,257)( 30,258)( 31,260)( 32,259)( 33,253)( 34,254)( 35,256)
( 36,255)( 37,249)( 38,250)( 39,252)( 40,251)( 41,245)( 42,246)( 43,248)
( 44,247)( 45,241)( 46,242)( 47,244)( 48,243)( 49,237)( 50,238)( 51,240)
( 52,239)( 53,233)( 54,234)( 55,236)( 56,235)( 57,229)( 58,230)( 59,232)
( 60,231)( 61,225)( 62,226)( 63,228)( 64,227)( 65,221)( 66,222)( 67,224)
( 68,223)( 69,217)( 70,218)( 71,220)( 72,219)( 73,213)( 74,214)( 75,216)
( 76,215)( 77,209)( 78,210)( 79,212)( 80,211)( 81,205)( 82,206)( 83,208)
( 84,207)( 85,201)( 86,202)( 87,204)( 88,203)( 89,197)( 90,198)( 91,200)
( 92,199)( 93,193)( 94,194)( 95,196)( 96,195)( 97,189)( 98,190)( 99,192)
(100,191)(101,185)(102,186)(103,188)(104,187)(105,181)(106,182)(107,184)
(108,183)(109,177)(110,178)(111,180)(112,179)(113,173)(114,174)(115,176)
(116,175)(117,169)(118,170)(119,172)(120,171)(121,165)(122,166)(123,168)
(124,167)(125,161)(126,162)(127,164)(128,163)(129,157)(130,158)(131,160)
(132,159)(133,153)(134,154)(135,156)(136,155)(137,149)(138,150)(139,152)
(140,151)(141,145)(142,146)(143,148)(144,147);;
s1 := ( 1, 5)( 2, 8)( 3, 7)( 4, 6)( 9,281)( 10,284)( 11,283)( 12,282)
( 13,277)( 14,280)( 15,279)( 16,278)( 17,273)( 18,276)( 19,275)( 20,274)
( 21,269)( 22,272)( 23,271)( 24,270)( 25,265)( 26,268)( 27,267)( 28,266)
( 29,261)( 30,264)( 31,263)( 32,262)( 33,257)( 34,260)( 35,259)( 36,258)
( 37,253)( 38,256)( 39,255)( 40,254)( 41,249)( 42,252)( 43,251)( 44,250)
( 45,245)( 46,248)( 47,247)( 48,246)( 49,241)( 50,244)( 51,243)( 52,242)
( 53,237)( 54,240)( 55,239)( 56,238)( 57,233)( 58,236)( 59,235)( 60,234)
( 61,229)( 62,232)( 63,231)( 64,230)( 65,225)( 66,228)( 67,227)( 68,226)
( 69,221)( 70,224)( 71,223)( 72,222)( 73,217)( 74,220)( 75,219)( 76,218)
( 77,213)( 78,216)( 79,215)( 80,214)( 81,209)( 82,212)( 83,211)( 84,210)
( 85,205)( 86,208)( 87,207)( 88,206)( 89,201)( 90,204)( 91,203)( 92,202)
( 93,197)( 94,200)( 95,199)( 96,198)( 97,193)( 98,196)( 99,195)(100,194)
(101,189)(102,192)(103,191)(104,190)(105,185)(106,188)(107,187)(108,186)
(109,181)(110,184)(111,183)(112,182)(113,177)(114,180)(115,179)(116,178)
(117,173)(118,176)(119,175)(120,174)(121,169)(122,172)(123,171)(124,170)
(125,165)(126,168)(127,167)(128,166)(129,161)(130,164)(131,163)(132,162)
(133,157)(134,160)(135,159)(136,158)(137,153)(138,156)(139,155)(140,154)
(141,149)(142,152)(143,151)(144,150)(146,148);;
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);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(284)!( 3, 4)( 5,281)( 6,282)( 7,284)( 8,283)( 9,277)( 10,278)
( 11,280)( 12,279)( 13,273)( 14,274)( 15,276)( 16,275)( 17,269)( 18,270)
( 19,272)( 20,271)( 21,265)( 22,266)( 23,268)( 24,267)( 25,261)( 26,262)
( 27,264)( 28,263)( 29,257)( 30,258)( 31,260)( 32,259)( 33,253)( 34,254)
( 35,256)( 36,255)( 37,249)( 38,250)( 39,252)( 40,251)( 41,245)( 42,246)
( 43,248)( 44,247)( 45,241)( 46,242)( 47,244)( 48,243)( 49,237)( 50,238)
( 51,240)( 52,239)( 53,233)( 54,234)( 55,236)( 56,235)( 57,229)( 58,230)
( 59,232)( 60,231)( 61,225)( 62,226)( 63,228)( 64,227)( 65,221)( 66,222)
( 67,224)( 68,223)( 69,217)( 70,218)( 71,220)( 72,219)( 73,213)( 74,214)
( 75,216)( 76,215)( 77,209)( 78,210)( 79,212)( 80,211)( 81,205)( 82,206)
( 83,208)( 84,207)( 85,201)( 86,202)( 87,204)( 88,203)( 89,197)( 90,198)
( 91,200)( 92,199)( 93,193)( 94,194)( 95,196)( 96,195)( 97,189)( 98,190)
( 99,192)(100,191)(101,185)(102,186)(103,188)(104,187)(105,181)(106,182)
(107,184)(108,183)(109,177)(110,178)(111,180)(112,179)(113,173)(114,174)
(115,176)(116,175)(117,169)(118,170)(119,172)(120,171)(121,165)(122,166)
(123,168)(124,167)(125,161)(126,162)(127,164)(128,163)(129,157)(130,158)
(131,160)(132,159)(133,153)(134,154)(135,156)(136,155)(137,149)(138,150)
(139,152)(140,151)(141,145)(142,146)(143,148)(144,147);
s1 := Sym(284)!( 1, 5)( 2, 8)( 3, 7)( 4, 6)( 9,281)( 10,284)( 11,283)
( 12,282)( 13,277)( 14,280)( 15,279)( 16,278)( 17,273)( 18,276)( 19,275)
( 20,274)( 21,269)( 22,272)( 23,271)( 24,270)( 25,265)( 26,268)( 27,267)
( 28,266)( 29,261)( 30,264)( 31,263)( 32,262)( 33,257)( 34,260)( 35,259)
( 36,258)( 37,253)( 38,256)( 39,255)( 40,254)( 41,249)( 42,252)( 43,251)
( 44,250)( 45,245)( 46,248)( 47,247)( 48,246)( 49,241)( 50,244)( 51,243)
( 52,242)( 53,237)( 54,240)( 55,239)( 56,238)( 57,233)( 58,236)( 59,235)
( 60,234)( 61,229)( 62,232)( 63,231)( 64,230)( 65,225)( 66,228)( 67,227)
( 68,226)( 69,221)( 70,224)( 71,223)( 72,222)( 73,217)( 74,220)( 75,219)
( 76,218)( 77,213)( 78,216)( 79,215)( 80,214)( 81,209)( 82,212)( 83,211)
( 84,210)( 85,205)( 86,208)( 87,207)( 88,206)( 89,201)( 90,204)( 91,203)
( 92,202)( 93,197)( 94,200)( 95,199)( 96,198)( 97,193)( 98,196)( 99,195)
(100,194)(101,189)(102,192)(103,191)(104,190)(105,185)(106,188)(107,187)
(108,186)(109,181)(110,184)(111,183)(112,182)(113,177)(114,180)(115,179)
(116,178)(117,173)(118,176)(119,175)(120,174)(121,169)(122,172)(123,171)
(124,170)(125,165)(126,168)(127,167)(128,166)(129,161)(130,164)(131,163)
(132,162)(133,157)(134,160)(135,159)(136,158)(137,153)(138,156)(139,155)
(140,154)(141,149)(142,152)(143,151)(144,150)(146,148);
s2 := Sym(284)!( 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);
poly := sub<Sym(284)|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 >;
References : None.
to this polytope