Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,40,8}

Atlas Canonical Name {2,40,8}*1280d

Overview

Group
SmallGroup(1280,150684)
Rank
4
Schläfli Type
{2,40,8}
Vertices, edges, …
2, 40, 160, 8
Order of s0s1s2s3
40
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

4-fold

5-fold

8-fold

10-fold

16-fold

20-fold

32-fold

40-fold

80-fold

Covers minimal covers in bold

None in this atlas.

Representations

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