Polytope of Type {2,2,5,5}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,5,5}*1280
if this polytope has a name.
Group : SmallGroup(1280,1116450)
Rank : 5
Schlafli Type : {2,2,5,5}
Number of vertices, edges, etc : 2, 2, 32, 80, 32
Order of s0s1s2s3s4 : 8
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
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 : {2,2,5,5}*640
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 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);;
s3 := ( 5,197)( 6,198)( 7,227)( 8,228)( 9,202)( 10,201)( 11,223)( 12,224)
( 13,210)( 14,209)( 15,215)( 16,216)( 17,206)( 18,205)( 19,220)( 20,219)
( 21,218)( 22,217)( 23,207)( 24,208)( 25,214)( 26,213)( 27,212)( 28,211)
( 29,221)( 30,222)( 31,203)( 32,204)( 33,226)( 34,225)( 35,199)( 36,200)
( 37,165)( 38,166)( 39,195)( 40,196)( 41,170)( 42,169)( 43,191)( 44,192)
( 45,178)( 46,177)( 47,183)( 48,184)( 49,174)( 50,173)( 51,188)( 52,187)
( 53,186)( 54,185)( 55,175)( 56,176)( 57,182)( 58,181)( 59,180)( 60,179)
( 61,189)( 62,190)( 63,171)( 64,172)( 65,194)( 66,193)( 67,167)( 68,168)
( 69,293)( 70,294)( 71,323)( 72,324)( 73,298)( 74,297)( 75,319)( 76,320)
( 77,306)( 78,305)( 79,311)( 80,312)( 81,302)( 82,301)( 83,316)( 84,315)
( 85,314)( 86,313)( 87,303)( 88,304)( 89,310)( 90,309)( 91,308)( 92,307)
( 93,317)( 94,318)( 95,299)( 96,300)( 97,322)( 98,321)( 99,295)(100,296)
(101,261)(102,262)(103,291)(104,292)(105,266)(106,265)(107,287)(108,288)
(109,274)(110,273)(111,279)(112,280)(113,270)(114,269)(115,284)(116,283)
(117,282)(118,281)(119,271)(120,272)(121,278)(122,277)(123,276)(124,275)
(125,285)(126,286)(127,267)(128,268)(129,290)(130,289)(131,263)(132,264)
(133,229)(134,230)(135,259)(136,260)(137,234)(138,233)(139,255)(140,256)
(141,242)(142,241)(143,247)(144,248)(145,238)(146,237)(147,252)(148,251)
(149,250)(150,249)(151,239)(152,240)(153,246)(154,245)(155,244)(156,243)
(157,253)(158,254)(159,235)(160,236)(161,258)(162,257)(163,231)(164,232);;
s4 := ( 5,195)( 6,196)( 7,176)( 8,175)( 9,170)( 10,169)( 11,181)( 12,182)
( 13,188)( 14,187)( 15,168)( 16,167)( 17,177)( 18,178)( 19,189)( 20,190)
( 21,171)( 22,172)( 23,183)( 24,184)( 25,194)( 26,193)( 27,174)( 28,173)
( 29,179)( 30,180)( 31,192)( 32,191)( 33,186)( 34,185)( 35,165)( 36,166)
( 37,323)( 38,324)( 39,304)( 40,303)( 41,298)( 42,297)( 43,309)( 44,310)
( 45,316)( 46,315)( 47,296)( 48,295)( 49,305)( 50,306)( 51,317)( 52,318)
( 53,299)( 54,300)( 55,311)( 56,312)( 57,322)( 58,321)( 59,302)( 60,301)
( 61,307)( 62,308)( 63,320)( 64,319)( 65,314)( 66,313)( 67,293)( 68,294)
( 69,291)( 70,292)( 71,272)( 72,271)( 73,266)( 74,265)( 75,277)( 76,278)
( 77,284)( 78,283)( 79,264)( 80,263)( 81,273)( 82,274)( 83,285)( 84,286)
( 85,267)( 86,268)( 87,279)( 88,280)( 89,290)( 90,289)( 91,270)( 92,269)
( 93,275)( 94,276)( 95,288)( 96,287)( 97,282)( 98,281)( 99,261)(100,262)
(101,259)(102,260)(103,240)(104,239)(105,234)(106,233)(107,245)(108,246)
(109,252)(110,251)(111,232)(112,231)(113,241)(114,242)(115,253)(116,254)
(117,235)(118,236)(119,247)(120,248)(121,258)(122,257)(123,238)(124,237)
(125,243)(126,244)(127,256)(128,255)(129,250)(130,249)(131,229)(132,230)
(133,227)(134,228)(135,208)(136,207)(137,202)(138,201)(139,213)(140,214)
(141,220)(142,219)(143,200)(144,199)(145,209)(146,210)(147,221)(148,222)
(149,203)(150,204)(151,215)(152,216)(153,226)(154,225)(155,206)(156,205)
(157,211)(158,212)(159,224)(160,223)(161,218)(162,217)(163,197)(164,198);;
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,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s4*s2*s3*s4*s3*s2*s3*s4*s3*s4*s2*s3*s2*s3*s4*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(324)!(1,2);
s1 := Sym(324)!(3,4);
s2 := 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);
s3 := Sym(324)!( 5,197)( 6,198)( 7,227)( 8,228)( 9,202)( 10,201)( 11,223)
( 12,224)( 13,210)( 14,209)( 15,215)( 16,216)( 17,206)( 18,205)( 19,220)
( 20,219)( 21,218)( 22,217)( 23,207)( 24,208)( 25,214)( 26,213)( 27,212)
( 28,211)( 29,221)( 30,222)( 31,203)( 32,204)( 33,226)( 34,225)( 35,199)
( 36,200)( 37,165)( 38,166)( 39,195)( 40,196)( 41,170)( 42,169)( 43,191)
( 44,192)( 45,178)( 46,177)( 47,183)( 48,184)( 49,174)( 50,173)( 51,188)
( 52,187)( 53,186)( 54,185)( 55,175)( 56,176)( 57,182)( 58,181)( 59,180)
( 60,179)( 61,189)( 62,190)( 63,171)( 64,172)( 65,194)( 66,193)( 67,167)
( 68,168)( 69,293)( 70,294)( 71,323)( 72,324)( 73,298)( 74,297)( 75,319)
( 76,320)( 77,306)( 78,305)( 79,311)( 80,312)( 81,302)( 82,301)( 83,316)
( 84,315)( 85,314)( 86,313)( 87,303)( 88,304)( 89,310)( 90,309)( 91,308)
( 92,307)( 93,317)( 94,318)( 95,299)( 96,300)( 97,322)( 98,321)( 99,295)
(100,296)(101,261)(102,262)(103,291)(104,292)(105,266)(106,265)(107,287)
(108,288)(109,274)(110,273)(111,279)(112,280)(113,270)(114,269)(115,284)
(116,283)(117,282)(118,281)(119,271)(120,272)(121,278)(122,277)(123,276)
(124,275)(125,285)(126,286)(127,267)(128,268)(129,290)(130,289)(131,263)
(132,264)(133,229)(134,230)(135,259)(136,260)(137,234)(138,233)(139,255)
(140,256)(141,242)(142,241)(143,247)(144,248)(145,238)(146,237)(147,252)
(148,251)(149,250)(150,249)(151,239)(152,240)(153,246)(154,245)(155,244)
(156,243)(157,253)(158,254)(159,235)(160,236)(161,258)(162,257)(163,231)
(164,232);
s4 := Sym(324)!( 5,195)( 6,196)( 7,176)( 8,175)( 9,170)( 10,169)( 11,181)
( 12,182)( 13,188)( 14,187)( 15,168)( 16,167)( 17,177)( 18,178)( 19,189)
( 20,190)( 21,171)( 22,172)( 23,183)( 24,184)( 25,194)( 26,193)( 27,174)
( 28,173)( 29,179)( 30,180)( 31,192)( 32,191)( 33,186)( 34,185)( 35,165)
( 36,166)( 37,323)( 38,324)( 39,304)( 40,303)( 41,298)( 42,297)( 43,309)
( 44,310)( 45,316)( 46,315)( 47,296)( 48,295)( 49,305)( 50,306)( 51,317)
( 52,318)( 53,299)( 54,300)( 55,311)( 56,312)( 57,322)( 58,321)( 59,302)
( 60,301)( 61,307)( 62,308)( 63,320)( 64,319)( 65,314)( 66,313)( 67,293)
( 68,294)( 69,291)( 70,292)( 71,272)( 72,271)( 73,266)( 74,265)( 75,277)
( 76,278)( 77,284)( 78,283)( 79,264)( 80,263)( 81,273)( 82,274)( 83,285)
( 84,286)( 85,267)( 86,268)( 87,279)( 88,280)( 89,290)( 90,289)( 91,270)
( 92,269)( 93,275)( 94,276)( 95,288)( 96,287)( 97,282)( 98,281)( 99,261)
(100,262)(101,259)(102,260)(103,240)(104,239)(105,234)(106,233)(107,245)
(108,246)(109,252)(110,251)(111,232)(112,231)(113,241)(114,242)(115,253)
(116,254)(117,235)(118,236)(119,247)(120,248)(121,258)(122,257)(123,238)
(124,237)(125,243)(126,244)(127,256)(128,255)(129,250)(130,249)(131,229)
(132,230)(133,227)(134,228)(135,208)(136,207)(137,202)(138,201)(139,213)
(140,214)(141,220)(142,219)(143,200)(144,199)(145,209)(146,210)(147,221)
(148,222)(149,203)(150,204)(151,215)(152,216)(153,226)(154,225)(155,206)
(156,205)(157,211)(158,212)(159,224)(160,223)(161,218)(162,217)(163,197)
(164,198);
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, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s4*s2*s3*s4*s3*s2*s3*s4*s3*s4*s2*s3*s2*s3*s4*s3*s2*s3 >;
to this polytope