Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1280,336974)
Rank
5
Schläfli Type
{2,20,4,4}
Vertices, edges, …
2, 20, 40, 8, 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 := (  3,203)(  4,207)(  5,206)(  6,205)(  7,204)(  8,208)(  9,212)( 10,211)( 11,210)( 12,209)( 13,213)( 14,217)( 15,216)( 16,215)( 17,214)( 18,218)( 19,222)( 20,221)( 21,220)( 22,219)( 23,223)( 24,227)( 25,226)( 26,225)( 27,224)( 28,228)( 29,232)( 30,231)( 31,230)( 32,229)( 33,233)( 34,237)( 35,236)( 36,235)( 37,234)( 38,238)( 39,242)( 40,241)( 41,240)( 42,239)( 43,163)( 44,167)( 45,166)( 46,165)( 47,164)( 48,168)( 49,172)( 50,171)( 51,170)( 52,169)( 53,173)( 54,177)( 55,176)( 56,175)( 57,174)( 58,178)( 59,182)( 60,181)( 61,180)( 62,179)( 63,183)( 64,187)( 65,186)( 66,185)( 67,184)( 68,188)( 69,192)( 70,191)( 71,190)( 72,189)( 73,193)( 74,197)( 75,196)( 76,195)( 77,194)( 78,198)( 79,202)( 80,201)( 81,200)( 82,199)( 83,288)( 84,292)( 85,291)( 86,290)( 87,289)( 88,283)( 89,287)( 90,286)( 91,285)( 92,284)( 93,298)( 94,302)( 95,301)( 96,300)( 97,299)( 98,293)( 99,297)(100,296)(101,295)(102,294)(103,308)(104,312)(105,311)(106,310)(107,309)(108,303)(109,307)(110,306)(111,305)(112,304)(113,318)(114,322)(115,321)(116,320)(117,319)(118,313)(119,317)(120,316)(121,315)(122,314)(123,248)(124,252)(125,251)(126,250)(127,249)(128,243)(129,247)(130,246)(131,245)(132,244)(133,258)(134,262)(135,261)(136,260)(137,259)(138,253)(139,257)(140,256)(141,255)(142,254)(143,268)(144,272)(145,271)(146,270)(147,269)(148,263)(149,267)(150,266)(151,265)(152,264)(153,278)(154,282)(155,281)(156,280)(157,279)(158,273)(159,277)(160,276)(161,275)(162,274);;
s2 := (  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);;
s3 := ( 43, 63)( 44, 64)( 45, 65)( 46, 66)( 47, 67)( 48, 68)( 49, 69)( 50, 70)( 51, 71)( 52, 72)( 53, 73)( 54, 74)( 55, 75)( 56, 76)( 57, 77)( 58, 78)( 59, 79)( 60, 80)( 61, 81)( 62, 82)( 83, 93)( 84, 94)( 85, 95)( 86, 96)( 87, 97)( 88, 98)( 89, 99)( 90,100)( 91,101)( 92,102)(103,113)(104,114)(105,115)(106,116)(107,117)(108,118)(109,119)(110,120)(111,121)(112,122)(123,153)(124,154)(125,155)(126,156)(127,157)(128,158)(129,159)(130,160)(131,161)(132,162)(133,143)(134,144)(135,145)(136,146)(137,147)(138,148)(139,149)(140,150)(141,151)(142,152)(163,183)(164,184)(165,185)(166,186)(167,187)(168,188)(169,189)(170,190)(171,191)(172,192)(173,193)(174,194)(175,195)(176,196)(177,197)(178,198)(179,199)(180,200)(181,201)(182,202)(243,273)(244,274)(245,275)(246,276)(247,277)(248,278)(249,279)(250,280)(251,281)(252,282)(253,263)(254,264)(255,265)(256,266)(257,267)(258,268)(259,269)(260,270)(261,271)(262,272)(283,293)(284,294)(285,295)(286,296)(287,297)(288,298)(289,299)(290,300)(291,301)(292,302)(303,313)(304,314)(305,315)(306,316)(307,317)(308,318)(309,319)(310,320)(311,321)(312,322);;
s4 := (  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);;
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*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(322)!(1,2);
s1 := Sym(322)!(  3,203)(  4,207)(  5,206)(  6,205)(  7,204)(  8,208)(  9,212)( 10,211)( 11,210)( 12,209)( 13,213)( 14,217)( 15,216)( 16,215)( 17,214)( 18,218)( 19,222)( 20,221)( 21,220)( 22,219)( 23,223)( 24,227)( 25,226)( 26,225)( 27,224)( 28,228)( 29,232)( 30,231)( 31,230)( 32,229)( 33,233)( 34,237)( 35,236)( 36,235)( 37,234)( 38,238)( 39,242)( 40,241)( 41,240)( 42,239)( 43,163)( 44,167)( 45,166)( 46,165)( 47,164)( 48,168)( 49,172)( 50,171)( 51,170)( 52,169)( 53,173)( 54,177)( 55,176)( 56,175)( 57,174)( 58,178)( 59,182)( 60,181)( 61,180)( 62,179)( 63,183)( 64,187)( 65,186)( 66,185)( 67,184)( 68,188)( 69,192)( 70,191)( 71,190)( 72,189)( 73,193)( 74,197)( 75,196)( 76,195)( 77,194)( 78,198)( 79,202)( 80,201)( 81,200)( 82,199)( 83,288)( 84,292)( 85,291)( 86,290)( 87,289)( 88,283)( 89,287)( 90,286)( 91,285)( 92,284)( 93,298)( 94,302)( 95,301)( 96,300)( 97,299)( 98,293)( 99,297)(100,296)(101,295)(102,294)(103,308)(104,312)(105,311)(106,310)(107,309)(108,303)(109,307)(110,306)(111,305)(112,304)(113,318)(114,322)(115,321)(116,320)(117,319)(118,313)(119,317)(120,316)(121,315)(122,314)(123,248)(124,252)(125,251)(126,250)(127,249)(128,243)(129,247)(130,246)(131,245)(132,244)(133,258)(134,262)(135,261)(136,260)(137,259)(138,253)(139,257)(140,256)(141,255)(142,254)(143,268)(144,272)(145,271)(146,270)(147,269)(148,263)(149,267)(150,266)(151,265)(152,264)(153,278)(154,282)(155,281)(156,280)(157,279)(158,273)(159,277)(160,276)(161,275)(162,274);
s2 := 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);
s3 := Sym(322)!( 43, 63)( 44, 64)( 45, 65)( 46, 66)( 47, 67)( 48, 68)( 49, 69)( 50, 70)( 51, 71)( 52, 72)( 53, 73)( 54, 74)( 55, 75)( 56, 76)( 57, 77)( 58, 78)( 59, 79)( 60, 80)( 61, 81)( 62, 82)( 83, 93)( 84, 94)( 85, 95)( 86, 96)( 87, 97)( 88, 98)( 89, 99)( 90,100)( 91,101)( 92,102)(103,113)(104,114)(105,115)(106,116)(107,117)(108,118)(109,119)(110,120)(111,121)(112,122)(123,153)(124,154)(125,155)(126,156)(127,157)(128,158)(129,159)(130,160)(131,161)(132,162)(133,143)(134,144)(135,145)(136,146)(137,147)(138,148)(139,149)(140,150)(141,151)(142,152)(163,183)(164,184)(165,185)(166,186)(167,187)(168,188)(169,189)(170,190)(171,191)(172,192)(173,193)(174,194)(175,195)(176,196)(177,197)(178,198)(179,199)(180,200)(181,201)(182,202)(243,273)(244,274)(245,275)(246,276)(247,277)(248,278)(249,279)(250,280)(251,281)(252,282)(253,263)(254,264)(255,265)(256,266)(257,267)(258,268)(259,269)(260,270)(261,271)(262,272)(283,293)(284,294)(285,295)(286,296)(287,297)(288,298)(289,299)(290,300)(291,301)(292,302)(303,313)(304,314)(305,315)(306,316)(307,317)(308,318)(309,319)(310,320)(311,321)(312,322);
s4 := 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);
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*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;