Polytope of Type {2,4,10,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,10,2}*1280a
if this polytope has a name.
Group : SmallGroup(1280,1116461)
Rank : 5
Schlafli Type : {2,4,10,2}
Number of vertices, edges, etc : 2, 16, 80, 40, 2
Order of s0s1s2s3s4 : 10
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
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) :
2-fold quotients : {2,4,5,2}*640
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 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)(293,294)(295,296)(297,298)(299,300)(301,302)(303,304)(305,306)
(307,308)(309,310)(311,312)(313,314)(315,316)(317,318)(319,320)(321,322);;
s2 := ( 3,163)( 4,173)( 5,176)( 6,170)( 7,167)( 8,177)( 9,172)( 10,166)
( 11,175)( 12,169)( 13,164)( 14,174)( 15,171)( 16,165)( 17,168)( 18,178)
( 19,227)( 20,237)( 21,240)( 22,234)( 23,231)( 24,241)( 25,236)( 26,230)
( 27,239)( 28,233)( 29,228)( 30,238)( 31,235)( 32,229)( 33,232)( 34,242)
( 35,211)( 36,221)( 37,224)( 38,218)( 39,215)( 40,225)( 41,220)( 42,214)
( 43,223)( 44,217)( 45,212)( 46,222)( 47,219)( 48,213)( 49,216)( 50,226)
( 51,195)( 52,205)( 53,208)( 54,202)( 55,199)( 56,209)( 57,204)( 58,198)
( 59,207)( 60,201)( 61,196)( 62,206)( 63,203)( 64,197)( 65,200)( 66,210)
( 67,179)( 68,189)( 69,192)( 70,186)( 71,183)( 72,193)( 73,188)( 74,182)
( 75,191)( 76,185)( 77,180)( 78,190)( 79,187)( 80,181)( 81,184)( 82,194)
( 83,243)( 84,253)( 85,256)( 86,250)( 87,247)( 88,257)( 89,252)( 90,246)
( 91,255)( 92,249)( 93,244)( 94,254)( 95,251)( 96,245)( 97,248)( 98,258)
( 99,307)(100,317)(101,320)(102,314)(103,311)(104,321)(105,316)(106,310)
(107,319)(108,313)(109,308)(110,318)(111,315)(112,309)(113,312)(114,322)
(115,291)(116,301)(117,304)(118,298)(119,295)(120,305)(121,300)(122,294)
(123,303)(124,297)(125,292)(126,302)(127,299)(128,293)(129,296)(130,306)
(131,275)(132,285)(133,288)(134,282)(135,279)(136,289)(137,284)(138,278)
(139,287)(140,281)(141,276)(142,286)(143,283)(144,277)(145,280)(146,290)
(147,259)(148,269)(149,272)(150,266)(151,263)(152,273)(153,268)(154,262)
(155,271)(156,265)(157,260)(158,270)(159,267)(160,261)(161,264)(162,274);;
s3 := ( 3,275)( 4,276)( 5,278)( 6,277)( 7,280)( 8,279)( 9,281)( 10,282)
( 11,290)( 12,289)( 13,287)( 14,288)( 15,285)( 16,286)( 17,284)( 18,283)
( 19,259)( 20,260)( 21,262)( 22,261)( 23,264)( 24,263)( 25,265)( 26,266)
( 27,274)( 28,273)( 29,271)( 30,272)( 31,269)( 32,270)( 33,268)( 34,267)
( 35,243)( 36,244)( 37,246)( 38,245)( 39,248)( 40,247)( 41,249)( 42,250)
( 43,258)( 44,257)( 45,255)( 46,256)( 47,253)( 48,254)( 49,252)( 50,251)
( 51,307)( 52,308)( 53,310)( 54,309)( 55,312)( 56,311)( 57,313)( 58,314)
( 59,322)( 60,321)( 61,319)( 62,320)( 63,317)( 64,318)( 65,316)( 66,315)
( 67,291)( 68,292)( 69,294)( 70,293)( 71,296)( 72,295)( 73,297)( 74,298)
( 75,306)( 76,305)( 77,303)( 78,304)( 79,301)( 80,302)( 81,300)( 82,299)
( 83,195)( 84,196)( 85,198)( 86,197)( 87,200)( 88,199)( 89,201)( 90,202)
( 91,210)( 92,209)( 93,207)( 94,208)( 95,205)( 96,206)( 97,204)( 98,203)
( 99,179)(100,180)(101,182)(102,181)(103,184)(104,183)(105,185)(106,186)
(107,194)(108,193)(109,191)(110,192)(111,189)(112,190)(113,188)(114,187)
(115,163)(116,164)(117,166)(118,165)(119,168)(120,167)(121,169)(122,170)
(123,178)(124,177)(125,175)(126,176)(127,173)(128,174)(129,172)(130,171)
(131,227)(132,228)(133,230)(134,229)(135,232)(136,231)(137,233)(138,234)
(139,242)(140,241)(141,239)(142,240)(143,237)(144,238)(145,236)(146,235)
(147,211)(148,212)(149,214)(150,213)(151,216)(152,215)(153,217)(154,218)
(155,226)(156,225)(157,223)(158,224)(159,221)(160,222)(161,220)(162,219);;
s4 := (323,324);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2,
s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(324)!(1,2);
s1 := Sym(324)!( 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)(293,294)(295,296)(297,298)(299,300)(301,302)(303,304)
(305,306)(307,308)(309,310)(311,312)(313,314)(315,316)(317,318)(319,320)
(321,322);
s2 := Sym(324)!( 3,163)( 4,173)( 5,176)( 6,170)( 7,167)( 8,177)( 9,172)
( 10,166)( 11,175)( 12,169)( 13,164)( 14,174)( 15,171)( 16,165)( 17,168)
( 18,178)( 19,227)( 20,237)( 21,240)( 22,234)( 23,231)( 24,241)( 25,236)
( 26,230)( 27,239)( 28,233)( 29,228)( 30,238)( 31,235)( 32,229)( 33,232)
( 34,242)( 35,211)( 36,221)( 37,224)( 38,218)( 39,215)( 40,225)( 41,220)
( 42,214)( 43,223)( 44,217)( 45,212)( 46,222)( 47,219)( 48,213)( 49,216)
( 50,226)( 51,195)( 52,205)( 53,208)( 54,202)( 55,199)( 56,209)( 57,204)
( 58,198)( 59,207)( 60,201)( 61,196)( 62,206)( 63,203)( 64,197)( 65,200)
( 66,210)( 67,179)( 68,189)( 69,192)( 70,186)( 71,183)( 72,193)( 73,188)
( 74,182)( 75,191)( 76,185)( 77,180)( 78,190)( 79,187)( 80,181)( 81,184)
( 82,194)( 83,243)( 84,253)( 85,256)( 86,250)( 87,247)( 88,257)( 89,252)
( 90,246)( 91,255)( 92,249)( 93,244)( 94,254)( 95,251)( 96,245)( 97,248)
( 98,258)( 99,307)(100,317)(101,320)(102,314)(103,311)(104,321)(105,316)
(106,310)(107,319)(108,313)(109,308)(110,318)(111,315)(112,309)(113,312)
(114,322)(115,291)(116,301)(117,304)(118,298)(119,295)(120,305)(121,300)
(122,294)(123,303)(124,297)(125,292)(126,302)(127,299)(128,293)(129,296)
(130,306)(131,275)(132,285)(133,288)(134,282)(135,279)(136,289)(137,284)
(138,278)(139,287)(140,281)(141,276)(142,286)(143,283)(144,277)(145,280)
(146,290)(147,259)(148,269)(149,272)(150,266)(151,263)(152,273)(153,268)
(154,262)(155,271)(156,265)(157,260)(158,270)(159,267)(160,261)(161,264)
(162,274);
s3 := Sym(324)!( 3,275)( 4,276)( 5,278)( 6,277)( 7,280)( 8,279)( 9,281)
( 10,282)( 11,290)( 12,289)( 13,287)( 14,288)( 15,285)( 16,286)( 17,284)
( 18,283)( 19,259)( 20,260)( 21,262)( 22,261)( 23,264)( 24,263)( 25,265)
( 26,266)( 27,274)( 28,273)( 29,271)( 30,272)( 31,269)( 32,270)( 33,268)
( 34,267)( 35,243)( 36,244)( 37,246)( 38,245)( 39,248)( 40,247)( 41,249)
( 42,250)( 43,258)( 44,257)( 45,255)( 46,256)( 47,253)( 48,254)( 49,252)
( 50,251)( 51,307)( 52,308)( 53,310)( 54,309)( 55,312)( 56,311)( 57,313)
( 58,314)( 59,322)( 60,321)( 61,319)( 62,320)( 63,317)( 64,318)( 65,316)
( 66,315)( 67,291)( 68,292)( 69,294)( 70,293)( 71,296)( 72,295)( 73,297)
( 74,298)( 75,306)( 76,305)( 77,303)( 78,304)( 79,301)( 80,302)( 81,300)
( 82,299)( 83,195)( 84,196)( 85,198)( 86,197)( 87,200)( 88,199)( 89,201)
( 90,202)( 91,210)( 92,209)( 93,207)( 94,208)( 95,205)( 96,206)( 97,204)
( 98,203)( 99,179)(100,180)(101,182)(102,181)(103,184)(104,183)(105,185)
(106,186)(107,194)(108,193)(109,191)(110,192)(111,189)(112,190)(113,188)
(114,187)(115,163)(116,164)(117,166)(118,165)(119,168)(120,167)(121,169)
(122,170)(123,178)(124,177)(125,175)(126,176)(127,173)(128,174)(129,172)
(130,171)(131,227)(132,228)(133,230)(134,229)(135,232)(136,231)(137,233)
(138,234)(139,242)(140,241)(141,239)(142,240)(143,237)(144,238)(145,236)
(146,235)(147,211)(148,212)(149,214)(150,213)(151,216)(152,215)(153,217)
(154,218)(155,226)(156,225)(157,223)(158,224)(159,221)(160,222)(161,220)
(162,219);
s4 := Sym(324)!(323,324);
poly := sub<Sym(324)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2,
s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope