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