Polytope of Type {2,5,8,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,5,8,2}*1280b
if this polytope has a name.
Group : SmallGroup(1280,1116450)
Rank : 5
Schlafli Type : {2,5,8,2}
Number of vertices, edges, etc : 2, 20, 80, 32, 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 : {2,5,4,2}*640
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3,163)( 4,164)( 5,183)( 6,184)( 7,189)( 8,190)( 9,177)( 10,178)
( 11,172)( 12,171)( 13,191)( 14,192)( 15,182)( 16,181)( 17,169)( 18,170)
( 19,187)( 20,188)( 21,176)( 22,175)( 23,165)( 24,166)( 25,186)( 26,185)
( 27,179)( 28,180)( 29,167)( 30,168)( 31,173)( 32,174)( 33,193)( 34,194)
( 35,291)( 36,292)( 37,311)( 38,312)( 39,317)( 40,318)( 41,305)( 42,306)
( 43,300)( 44,299)( 45,319)( 46,320)( 47,310)( 48,309)( 49,297)( 50,298)
( 51,315)( 52,316)( 53,304)( 54,303)( 55,293)( 56,294)( 57,314)( 58,313)
( 59,307)( 60,308)( 61,295)( 62,296)( 63,301)( 64,302)( 65,321)( 66,322)
( 67,259)( 68,260)( 69,279)( 70,280)( 71,285)( 72,286)( 73,273)( 74,274)
( 75,268)( 76,267)( 77,287)( 78,288)( 79,278)( 80,277)( 81,265)( 82,266)
( 83,283)( 84,284)( 85,272)( 86,271)( 87,261)( 88,262)( 89,282)( 90,281)
( 91,275)( 92,276)( 93,263)( 94,264)( 95,269)( 96,270)( 97,289)( 98,290)
( 99,227)(100,228)(101,247)(102,248)(103,253)(104,254)(105,241)(106,242)
(107,236)(108,235)(109,255)(110,256)(111,246)(112,245)(113,233)(114,234)
(115,251)(116,252)(117,240)(118,239)(119,229)(120,230)(121,250)(122,249)
(123,243)(124,244)(125,231)(126,232)(127,237)(128,238)(129,257)(130,258)
(131,195)(132,196)(133,215)(134,216)(135,221)(136,222)(137,209)(138,210)
(139,204)(140,203)(141,223)(142,224)(143,214)(144,213)(145,201)(146,202)
(147,219)(148,220)(149,208)(150,207)(151,197)(152,198)(153,218)(154,217)
(155,211)(156,212)(157,199)(158,200)(159,205)(160,206)(161,225)(162,226);;
s2 := ( 3,195)( 4,196)( 5,225)( 6,226)( 7,200)( 8,199)( 9,221)( 10,222)
( 11,208)( 12,207)( 13,213)( 14,214)( 15,204)( 16,203)( 17,218)( 18,217)
( 19,216)( 20,215)( 21,205)( 22,206)( 23,212)( 24,211)( 25,210)( 26,209)
( 27,219)( 28,220)( 29,201)( 30,202)( 31,224)( 32,223)( 33,197)( 34,198)
( 35,163)( 36,164)( 37,193)( 38,194)( 39,168)( 40,167)( 41,189)( 42,190)
( 43,176)( 44,175)( 45,181)( 46,182)( 47,172)( 48,171)( 49,186)( 50,185)
( 51,184)( 52,183)( 53,173)( 54,174)( 55,180)( 56,179)( 57,178)( 58,177)
( 59,187)( 60,188)( 61,169)( 62,170)( 63,192)( 64,191)( 65,165)( 66,166)
( 67,291)( 68,292)( 69,321)( 70,322)( 71,296)( 72,295)( 73,317)( 74,318)
( 75,304)( 76,303)( 77,309)( 78,310)( 79,300)( 80,299)( 81,314)( 82,313)
( 83,312)( 84,311)( 85,301)( 86,302)( 87,308)( 88,307)( 89,306)( 90,305)
( 91,315)( 92,316)( 93,297)( 94,298)( 95,320)( 96,319)( 97,293)( 98,294)
( 99,259)(100,260)(101,289)(102,290)(103,264)(104,263)(105,285)(106,286)
(107,272)(108,271)(109,277)(110,278)(111,268)(112,267)(113,282)(114,281)
(115,280)(116,279)(117,269)(118,270)(119,276)(120,275)(121,274)(122,273)
(123,283)(124,284)(125,265)(126,266)(127,288)(128,287)(129,261)(130,262)
(131,227)(132,228)(133,257)(134,258)(135,232)(136,231)(137,253)(138,254)
(139,240)(140,239)(141,245)(142,246)(143,236)(144,235)(145,250)(146,249)
(147,248)(148,247)(149,237)(150,238)(151,244)(152,243)(153,242)(154,241)
(155,251)(156,252)(157,233)(158,234)(159,256)(160,255)(161,229)(162,230);;
s3 := ( 3, 34)( 4, 33)( 5, 31)( 6, 32)( 7, 29)( 8, 30)( 9, 28)( 10, 27)
( 11, 26)( 12, 25)( 13, 23)( 14, 24)( 15, 21)( 16, 22)( 17, 20)( 18, 19)
( 35, 66)( 36, 65)( 37, 63)( 38, 64)( 39, 61)( 40, 62)( 41, 60)( 42, 59)
( 43, 58)( 44, 57)( 45, 55)( 46, 56)( 47, 53)( 48, 54)( 49, 52)( 50, 51)
( 67, 98)( 68, 97)( 69, 95)( 70, 96)( 71, 93)( 72, 94)( 73, 92)( 74, 91)
( 75, 90)( 76, 89)( 77, 87)( 78, 88)( 79, 85)( 80, 86)( 81, 84)( 82, 83)
( 99,130)(100,129)(101,127)(102,128)(103,125)(104,126)(105,124)(106,123)
(107,122)(108,121)(109,119)(110,120)(111,117)(112,118)(113,116)(114,115)
(131,162)(132,161)(133,159)(134,160)(135,157)(136,158)(137,156)(138,155)
(139,154)(140,153)(141,151)(142,152)(143,149)(144,150)(145,148)(146,147)
(163,194)(164,193)(165,191)(166,192)(167,189)(168,190)(169,188)(170,187)
(171,186)(172,185)(173,183)(174,184)(175,181)(176,182)(177,180)(178,179)
(195,226)(196,225)(197,223)(198,224)(199,221)(200,222)(201,220)(202,219)
(203,218)(204,217)(205,215)(206,216)(207,213)(208,214)(209,212)(210,211)
(227,258)(228,257)(229,255)(230,256)(231,253)(232,254)(233,252)(234,251)
(235,250)(236,249)(237,247)(238,248)(239,245)(240,246)(241,244)(242,243)
(259,290)(260,289)(261,287)(262,288)(263,285)(264,286)(265,284)(266,283)
(267,282)(268,281)(269,279)(270,280)(271,277)(272,278)(273,276)(274,275)
(291,322)(292,321)(293,319)(294,320)(295,317)(296,318)(297,316)(298,315)
(299,314)(300,313)(301,311)(302,312)(303,309)(304,310)(305,308)(306,307);;
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,
s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2,
s1*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s1*s2*s1*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(324)!(1,2);
s1 := Sym(324)!( 3,163)( 4,164)( 5,183)( 6,184)( 7,189)( 8,190)( 9,177)
( 10,178)( 11,172)( 12,171)( 13,191)( 14,192)( 15,182)( 16,181)( 17,169)
( 18,170)( 19,187)( 20,188)( 21,176)( 22,175)( 23,165)( 24,166)( 25,186)
( 26,185)( 27,179)( 28,180)( 29,167)( 30,168)( 31,173)( 32,174)( 33,193)
( 34,194)( 35,291)( 36,292)( 37,311)( 38,312)( 39,317)( 40,318)( 41,305)
( 42,306)( 43,300)( 44,299)( 45,319)( 46,320)( 47,310)( 48,309)( 49,297)
( 50,298)( 51,315)( 52,316)( 53,304)( 54,303)( 55,293)( 56,294)( 57,314)
( 58,313)( 59,307)( 60,308)( 61,295)( 62,296)( 63,301)( 64,302)( 65,321)
( 66,322)( 67,259)( 68,260)( 69,279)( 70,280)( 71,285)( 72,286)( 73,273)
( 74,274)( 75,268)( 76,267)( 77,287)( 78,288)( 79,278)( 80,277)( 81,265)
( 82,266)( 83,283)( 84,284)( 85,272)( 86,271)( 87,261)( 88,262)( 89,282)
( 90,281)( 91,275)( 92,276)( 93,263)( 94,264)( 95,269)( 96,270)( 97,289)
( 98,290)( 99,227)(100,228)(101,247)(102,248)(103,253)(104,254)(105,241)
(106,242)(107,236)(108,235)(109,255)(110,256)(111,246)(112,245)(113,233)
(114,234)(115,251)(116,252)(117,240)(118,239)(119,229)(120,230)(121,250)
(122,249)(123,243)(124,244)(125,231)(126,232)(127,237)(128,238)(129,257)
(130,258)(131,195)(132,196)(133,215)(134,216)(135,221)(136,222)(137,209)
(138,210)(139,204)(140,203)(141,223)(142,224)(143,214)(144,213)(145,201)
(146,202)(147,219)(148,220)(149,208)(150,207)(151,197)(152,198)(153,218)
(154,217)(155,211)(156,212)(157,199)(158,200)(159,205)(160,206)(161,225)
(162,226);
s2 := Sym(324)!( 3,195)( 4,196)( 5,225)( 6,226)( 7,200)( 8,199)( 9,221)
( 10,222)( 11,208)( 12,207)( 13,213)( 14,214)( 15,204)( 16,203)( 17,218)
( 18,217)( 19,216)( 20,215)( 21,205)( 22,206)( 23,212)( 24,211)( 25,210)
( 26,209)( 27,219)( 28,220)( 29,201)( 30,202)( 31,224)( 32,223)( 33,197)
( 34,198)( 35,163)( 36,164)( 37,193)( 38,194)( 39,168)( 40,167)( 41,189)
( 42,190)( 43,176)( 44,175)( 45,181)( 46,182)( 47,172)( 48,171)( 49,186)
( 50,185)( 51,184)( 52,183)( 53,173)( 54,174)( 55,180)( 56,179)( 57,178)
( 58,177)( 59,187)( 60,188)( 61,169)( 62,170)( 63,192)( 64,191)( 65,165)
( 66,166)( 67,291)( 68,292)( 69,321)( 70,322)( 71,296)( 72,295)( 73,317)
( 74,318)( 75,304)( 76,303)( 77,309)( 78,310)( 79,300)( 80,299)( 81,314)
( 82,313)( 83,312)( 84,311)( 85,301)( 86,302)( 87,308)( 88,307)( 89,306)
( 90,305)( 91,315)( 92,316)( 93,297)( 94,298)( 95,320)( 96,319)( 97,293)
( 98,294)( 99,259)(100,260)(101,289)(102,290)(103,264)(104,263)(105,285)
(106,286)(107,272)(108,271)(109,277)(110,278)(111,268)(112,267)(113,282)
(114,281)(115,280)(116,279)(117,269)(118,270)(119,276)(120,275)(121,274)
(122,273)(123,283)(124,284)(125,265)(126,266)(127,288)(128,287)(129,261)
(130,262)(131,227)(132,228)(133,257)(134,258)(135,232)(136,231)(137,253)
(138,254)(139,240)(140,239)(141,245)(142,246)(143,236)(144,235)(145,250)
(146,249)(147,248)(148,247)(149,237)(150,238)(151,244)(152,243)(153,242)
(154,241)(155,251)(156,252)(157,233)(158,234)(159,256)(160,255)(161,229)
(162,230);
s3 := Sym(324)!( 3, 34)( 4, 33)( 5, 31)( 6, 32)( 7, 29)( 8, 30)( 9, 28)
( 10, 27)( 11, 26)( 12, 25)( 13, 23)( 14, 24)( 15, 21)( 16, 22)( 17, 20)
( 18, 19)( 35, 66)( 36, 65)( 37, 63)( 38, 64)( 39, 61)( 40, 62)( 41, 60)
( 42, 59)( 43, 58)( 44, 57)( 45, 55)( 46, 56)( 47, 53)( 48, 54)( 49, 52)
( 50, 51)( 67, 98)( 68, 97)( 69, 95)( 70, 96)( 71, 93)( 72, 94)( 73, 92)
( 74, 91)( 75, 90)( 76, 89)( 77, 87)( 78, 88)( 79, 85)( 80, 86)( 81, 84)
( 82, 83)( 99,130)(100,129)(101,127)(102,128)(103,125)(104,126)(105,124)
(106,123)(107,122)(108,121)(109,119)(110,120)(111,117)(112,118)(113,116)
(114,115)(131,162)(132,161)(133,159)(134,160)(135,157)(136,158)(137,156)
(138,155)(139,154)(140,153)(141,151)(142,152)(143,149)(144,150)(145,148)
(146,147)(163,194)(164,193)(165,191)(166,192)(167,189)(168,190)(169,188)
(170,187)(171,186)(172,185)(173,183)(174,184)(175,181)(176,182)(177,180)
(178,179)(195,226)(196,225)(197,223)(198,224)(199,221)(200,222)(201,220)
(202,219)(203,218)(204,217)(205,215)(206,216)(207,213)(208,214)(209,212)
(210,211)(227,258)(228,257)(229,255)(230,256)(231,253)(232,254)(233,252)
(234,251)(235,250)(236,249)(237,247)(238,248)(239,245)(240,246)(241,244)
(242,243)(259,290)(260,289)(261,287)(262,288)(263,285)(264,286)(265,284)
(266,283)(267,282)(268,281)(269,279)(270,280)(271,277)(272,278)(273,276)
(274,275)(291,322)(292,321)(293,319)(294,320)(295,317)(296,318)(297,316)
(298,315)(299,314)(300,313)(301,311)(302,312)(303,309)(304,310)(305,308)
(306,307);
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, s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2,
s1*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s1*s2*s1*s3*s2*s3 >;
to this polytope