Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,4,20,4}

Atlas Canonical Name {2,4,20,4}*1280

Overview

Group
SmallGroup(1280,336975)
Rank
5
Schläfli Type
{2,4,20,4}
Vertices, edges, …
2, 4, 40, 40, 4
Order of s0s1s2s3s4
20
Order of s0s1s2s3s4s3s2s1
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

40-fold

Covers minimal covers in bold

None in this atlas.

Representations

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