Polytope of Type {2,2,8,5}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,8,5}*1280a
if this polytope has a name.
Group : SmallGroup(1280,1116450)
Rank : 5
Schlafli Type : {2,2,8,5}
Number of vertices, edges, etc : 2, 2, 32, 80, 20
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, 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);;
s3 := ( 5,165)( 6,166)( 7,185)( 8,186)( 9,191)( 10,192)( 11,179)( 12,180)
( 13,174)( 14,173)( 15,193)( 16,194)( 17,184)( 18,183)( 19,171)( 20,172)
( 21,189)( 22,190)( 23,178)( 24,177)( 25,167)( 26,168)( 27,188)( 28,187)
( 29,181)( 30,182)( 31,169)( 32,170)( 33,175)( 34,176)( 35,195)( 36,196)
( 37,293)( 38,294)( 39,313)( 40,314)( 41,319)( 42,320)( 43,307)( 44,308)
( 45,302)( 46,301)( 47,321)( 48,322)( 49,312)( 50,311)( 51,299)( 52,300)
( 53,317)( 54,318)( 55,306)( 56,305)( 57,295)( 58,296)( 59,316)( 60,315)
( 61,309)( 62,310)( 63,297)( 64,298)( 65,303)( 66,304)( 67,323)( 68,324)
( 69,261)( 70,262)( 71,281)( 72,282)( 73,287)( 74,288)( 75,275)( 76,276)
( 77,270)( 78,269)( 79,289)( 80,290)( 81,280)( 82,279)( 83,267)( 84,268)
( 85,285)( 86,286)( 87,274)( 88,273)( 89,263)( 90,264)( 91,284)( 92,283)
( 93,277)( 94,278)( 95,265)( 96,266)( 97,271)( 98,272)( 99,291)(100,292)
(101,229)(102,230)(103,249)(104,250)(105,255)(106,256)(107,243)(108,244)
(109,238)(110,237)(111,257)(112,258)(113,248)(114,247)(115,235)(116,236)
(117,253)(118,254)(119,242)(120,241)(121,231)(122,232)(123,252)(124,251)
(125,245)(126,246)(127,233)(128,234)(129,239)(130,240)(131,259)(132,260)
(133,197)(134,198)(135,217)(136,218)(137,223)(138,224)(139,211)(140,212)
(141,206)(142,205)(143,225)(144,226)(145,216)(146,215)(147,203)(148,204)
(149,221)(150,222)(151,210)(152,209)(153,199)(154,200)(155,220)(156,219)
(157,213)(158,214)(159,201)(160,202)(161,207)(162,208)(163,227)(164,228);;
s4 := ( 5,229)( 6,230)( 7,231)( 8,232)( 9,236)( 10,235)( 11,234)( 12,233)
( 13,239)( 14,240)( 15,237)( 16,238)( 17,242)( 18,241)( 19,244)( 20,243)
( 21,260)( 22,259)( 23,258)( 24,257)( 25,254)( 26,253)( 27,256)( 28,255)
( 29,250)( 30,249)( 31,252)( 32,251)( 33,248)( 34,247)( 35,246)( 36,245)
( 37,197)( 38,198)( 39,199)( 40,200)( 41,204)( 42,203)( 43,202)( 44,201)
( 45,207)( 46,208)( 47,205)( 48,206)( 49,210)( 50,209)( 51,212)( 52,211)
( 53,228)( 54,227)( 55,226)( 56,225)( 57,222)( 58,221)( 59,224)( 60,223)
( 61,218)( 62,217)( 63,220)( 64,219)( 65,216)( 66,215)( 67,214)( 68,213)
( 69,165)( 70,166)( 71,167)( 72,168)( 73,172)( 74,171)( 75,170)( 76,169)
( 77,175)( 78,176)( 79,173)( 80,174)( 81,178)( 82,177)( 83,180)( 84,179)
( 85,196)( 86,195)( 87,194)( 88,193)( 89,190)( 90,189)( 91,192)( 92,191)
( 93,186)( 94,185)( 95,188)( 96,187)( 97,184)( 98,183)( 99,182)(100,181)
(101,293)(102,294)(103,295)(104,296)(105,300)(106,299)(107,298)(108,297)
(109,303)(110,304)(111,301)(112,302)(113,306)(114,305)(115,308)(116,307)
(117,324)(118,323)(119,322)(120,321)(121,318)(122,317)(123,320)(124,319)
(125,314)(126,313)(127,316)(128,315)(129,312)(130,311)(131,310)(132,309)
(133,261)(134,262)(135,263)(136,264)(137,268)(138,267)(139,266)(140,265)
(141,271)(142,272)(143,269)(144,270)(145,274)(146,273)(147,276)(148,275)
(149,292)(150,291)(151,290)(152,289)(153,286)(154,285)(155,288)(156,287)
(157,282)(158,281)(159,284)(160,283)(161,280)(162,279)(163,278)(164,277);;
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, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s2*s3*s2*s3*s4*s3*s2*s3*s2*s3,
s4*s3*s2*s4*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s4*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(324)!(1,2);
s1 := Sym(324)!(3,4);
s2 := Sym(324)!( 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);
s3 := Sym(324)!( 5,165)( 6,166)( 7,185)( 8,186)( 9,191)( 10,192)( 11,179)
( 12,180)( 13,174)( 14,173)( 15,193)( 16,194)( 17,184)( 18,183)( 19,171)
( 20,172)( 21,189)( 22,190)( 23,178)( 24,177)( 25,167)( 26,168)( 27,188)
( 28,187)( 29,181)( 30,182)( 31,169)( 32,170)( 33,175)( 34,176)( 35,195)
( 36,196)( 37,293)( 38,294)( 39,313)( 40,314)( 41,319)( 42,320)( 43,307)
( 44,308)( 45,302)( 46,301)( 47,321)( 48,322)( 49,312)( 50,311)( 51,299)
( 52,300)( 53,317)( 54,318)( 55,306)( 56,305)( 57,295)( 58,296)( 59,316)
( 60,315)( 61,309)( 62,310)( 63,297)( 64,298)( 65,303)( 66,304)( 67,323)
( 68,324)( 69,261)( 70,262)( 71,281)( 72,282)( 73,287)( 74,288)( 75,275)
( 76,276)( 77,270)( 78,269)( 79,289)( 80,290)( 81,280)( 82,279)( 83,267)
( 84,268)( 85,285)( 86,286)( 87,274)( 88,273)( 89,263)( 90,264)( 91,284)
( 92,283)( 93,277)( 94,278)( 95,265)( 96,266)( 97,271)( 98,272)( 99,291)
(100,292)(101,229)(102,230)(103,249)(104,250)(105,255)(106,256)(107,243)
(108,244)(109,238)(110,237)(111,257)(112,258)(113,248)(114,247)(115,235)
(116,236)(117,253)(118,254)(119,242)(120,241)(121,231)(122,232)(123,252)
(124,251)(125,245)(126,246)(127,233)(128,234)(129,239)(130,240)(131,259)
(132,260)(133,197)(134,198)(135,217)(136,218)(137,223)(138,224)(139,211)
(140,212)(141,206)(142,205)(143,225)(144,226)(145,216)(146,215)(147,203)
(148,204)(149,221)(150,222)(151,210)(152,209)(153,199)(154,200)(155,220)
(156,219)(157,213)(158,214)(159,201)(160,202)(161,207)(162,208)(163,227)
(164,228);
s4 := Sym(324)!( 5,229)( 6,230)( 7,231)( 8,232)( 9,236)( 10,235)( 11,234)
( 12,233)( 13,239)( 14,240)( 15,237)( 16,238)( 17,242)( 18,241)( 19,244)
( 20,243)( 21,260)( 22,259)( 23,258)( 24,257)( 25,254)( 26,253)( 27,256)
( 28,255)( 29,250)( 30,249)( 31,252)( 32,251)( 33,248)( 34,247)( 35,246)
( 36,245)( 37,197)( 38,198)( 39,199)( 40,200)( 41,204)( 42,203)( 43,202)
( 44,201)( 45,207)( 46,208)( 47,205)( 48,206)( 49,210)( 50,209)( 51,212)
( 52,211)( 53,228)( 54,227)( 55,226)( 56,225)( 57,222)( 58,221)( 59,224)
( 60,223)( 61,218)( 62,217)( 63,220)( 64,219)( 65,216)( 66,215)( 67,214)
( 68,213)( 69,165)( 70,166)( 71,167)( 72,168)( 73,172)( 74,171)( 75,170)
( 76,169)( 77,175)( 78,176)( 79,173)( 80,174)( 81,178)( 82,177)( 83,180)
( 84,179)( 85,196)( 86,195)( 87,194)( 88,193)( 89,190)( 90,189)( 91,192)
( 92,191)( 93,186)( 94,185)( 95,188)( 96,187)( 97,184)( 98,183)( 99,182)
(100,181)(101,293)(102,294)(103,295)(104,296)(105,300)(106,299)(107,298)
(108,297)(109,303)(110,304)(111,301)(112,302)(113,306)(114,305)(115,308)
(116,307)(117,324)(118,323)(119,322)(120,321)(121,318)(122,317)(123,320)
(124,319)(125,314)(126,313)(127,316)(128,315)(129,312)(130,311)(131,310)
(132,309)(133,261)(134,262)(135,263)(136,264)(137,268)(138,267)(139,266)
(140,265)(141,271)(142,272)(143,269)(144,270)(145,274)(146,273)(147,276)
(148,275)(149,292)(150,291)(151,290)(152,289)(153,286)(154,285)(155,288)
(156,287)(157,282)(158,281)(159,284)(160,283)(161,280)(162,279)(163,278)
(164,277);
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,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s2*s3*s2*s3*s4*s3*s2*s3*s2*s3,
s4*s3*s2*s4*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s4*s3*s2 >;
to this polytope