Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,2,4,10}

Atlas Canonical Name {2,2,4,10}*1280a

Overview

Group
SmallGroup(1280,1116461)
Rank
5
Schläfli Type
{2,2,4,10}
Vertices, edges, …
2, 2, 16, 80, 40
Order of s0s1s2s3s4
10
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

Covers minimal covers in bold

None in this atlas.

Representations

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 >;