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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,4,20}*1280
if this polytope has a name.
Group : SmallGroup(1280,336974)
Rank : 5
Schlafli Type : {2,4,4,20}
Number of vertices, edges, etc : 2, 4, 8, 40, 20
Order of s0s1s2s3s4 : 20
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 : {2,2,4,20}*640, {2,4,2,20}*640, {2,4,4,10}*640
   4-fold quotients : {2,2,2,20}*320, {2,2,4,10}*320, {2,4,2,10}*320
   5-fold quotients : {2,4,4,4}*256
   8-fold quotients : {2,4,2,5}*160, {2,2,2,10}*160
   10-fold quotients : {2,2,4,4}*128, {2,4,4,2}*128, {2,4,2,4}*128
   16-fold quotients : {2,2,2,5}*80
   20-fold quotients : {2,2,2,4}*64, {2,2,4,2}*64, {2,4,2,2}*64
   40-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
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 := ( 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);;
s3 := (  3, 83)(  4, 87)(  5, 86)(  6, 85)(  7, 84)(  8, 88)(  9, 92)( 10, 91)
( 11, 90)( 12, 89)( 13, 93)( 14, 97)( 15, 96)( 16, 95)( 17, 94)( 18, 98)
( 19,102)( 20,101)( 21,100)( 22, 99)( 23,103)( 24,107)( 25,106)( 26,105)
( 27,104)( 28,108)( 29,112)( 30,111)( 31,110)( 32,109)( 33,113)( 34,117)
( 35,116)( 36,115)( 37,114)( 38,118)( 39,122)( 40,121)( 41,120)( 42,119)
( 43,123)( 44,127)( 45,126)( 46,125)( 47,124)( 48,128)( 49,132)( 50,131)
( 51,130)( 52,129)( 53,133)( 54,137)( 55,136)( 56,135)( 57,134)( 58,138)
( 59,142)( 60,141)( 61,140)( 62,139)( 63,143)( 64,147)( 65,146)( 66,145)
( 67,144)( 68,148)( 69,152)( 70,151)( 71,150)( 72,149)( 73,153)( 74,157)
( 75,156)( 76,155)( 77,154)( 78,158)( 79,162)( 80,161)( 81,160)( 82,159)
(163,243)(164,247)(165,246)(166,245)(167,244)(168,248)(169,252)(170,251)
(171,250)(172,249)(173,253)(174,257)(175,256)(176,255)(177,254)(178,258)
(179,262)(180,261)(181,260)(182,259)(183,263)(184,267)(185,266)(186,265)
(187,264)(188,268)(189,272)(190,271)(191,270)(192,269)(193,273)(194,277)
(195,276)(196,275)(197,274)(198,278)(199,282)(200,281)(201,280)(202,279)
(203,283)(204,287)(205,286)(206,285)(207,284)(208,288)(209,292)(210,291)
(211,290)(212,289)(213,293)(214,297)(215,296)(216,295)(217,294)(218,298)
(219,302)(220,301)(221,300)(222,299)(223,303)(224,307)(225,306)(226,305)
(227,304)(228,308)(229,312)(230,311)(231,310)(232,309)(233,313)(234,317)
(235,316)(236,315)(237,314)(238,318)(239,322)(240,321)(241,320)(242,319);;
s4 := (  3,204)(  4,203)(  5,207)(  6,206)(  7,205)(  8,209)(  9,208)( 10,212)
( 11,211)( 12,210)( 13,214)( 14,213)( 15,217)( 16,216)( 17,215)( 18,219)
( 19,218)( 20,222)( 21,221)( 22,220)( 23,224)( 24,223)( 25,227)( 26,226)
( 27,225)( 28,229)( 29,228)( 30,232)( 31,231)( 32,230)( 33,234)( 34,233)
( 35,237)( 36,236)( 37,235)( 38,239)( 39,238)( 40,242)( 41,241)( 42,240)
( 43,164)( 44,163)( 45,167)( 46,166)( 47,165)( 48,169)( 49,168)( 50,172)
( 51,171)( 52,170)( 53,174)( 54,173)( 55,177)( 56,176)( 57,175)( 58,179)
( 59,178)( 60,182)( 61,181)( 62,180)( 63,184)( 64,183)( 65,187)( 66,186)
( 67,185)( 68,189)( 69,188)( 70,192)( 71,191)( 72,190)( 73,194)( 74,193)
( 75,197)( 76,196)( 77,195)( 78,199)( 79,198)( 80,202)( 81,201)( 82,200)
( 83,289)( 84,288)( 85,292)( 86,291)( 87,290)( 88,284)( 89,283)( 90,287)
( 91,286)( 92,285)( 93,299)( 94,298)( 95,302)( 96,301)( 97,300)( 98,294)
( 99,293)(100,297)(101,296)(102,295)(103,309)(104,308)(105,312)(106,311)
(107,310)(108,304)(109,303)(110,307)(111,306)(112,305)(113,319)(114,318)
(115,322)(116,321)(117,320)(118,314)(119,313)(120,317)(121,316)(122,315)
(123,249)(124,248)(125,252)(126,251)(127,250)(128,244)(129,243)(130,247)
(131,246)(132,245)(133,259)(134,258)(135,262)(136,261)(137,260)(138,254)
(139,253)(140,257)(141,256)(142,255)(143,269)(144,268)(145,272)(146,271)
(147,270)(148,264)(149,263)(150,267)(151,266)(152,265)(153,279)(154,278)
(155,282)(156,281)(157,280)(158,274)(159,273)(160,277)(161,276)(162,275);;
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*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*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(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)!( 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);
s3 := Sym(322)!(  3, 83)(  4, 87)(  5, 86)(  6, 85)(  7, 84)(  8, 88)(  9, 92)
( 10, 91)( 11, 90)( 12, 89)( 13, 93)( 14, 97)( 15, 96)( 16, 95)( 17, 94)
( 18, 98)( 19,102)( 20,101)( 21,100)( 22, 99)( 23,103)( 24,107)( 25,106)
( 26,105)( 27,104)( 28,108)( 29,112)( 30,111)( 31,110)( 32,109)( 33,113)
( 34,117)( 35,116)( 36,115)( 37,114)( 38,118)( 39,122)( 40,121)( 41,120)
( 42,119)( 43,123)( 44,127)( 45,126)( 46,125)( 47,124)( 48,128)( 49,132)
( 50,131)( 51,130)( 52,129)( 53,133)( 54,137)( 55,136)( 56,135)( 57,134)
( 58,138)( 59,142)( 60,141)( 61,140)( 62,139)( 63,143)( 64,147)( 65,146)
( 66,145)( 67,144)( 68,148)( 69,152)( 70,151)( 71,150)( 72,149)( 73,153)
( 74,157)( 75,156)( 76,155)( 77,154)( 78,158)( 79,162)( 80,161)( 81,160)
( 82,159)(163,243)(164,247)(165,246)(166,245)(167,244)(168,248)(169,252)
(170,251)(171,250)(172,249)(173,253)(174,257)(175,256)(176,255)(177,254)
(178,258)(179,262)(180,261)(181,260)(182,259)(183,263)(184,267)(185,266)
(186,265)(187,264)(188,268)(189,272)(190,271)(191,270)(192,269)(193,273)
(194,277)(195,276)(196,275)(197,274)(198,278)(199,282)(200,281)(201,280)
(202,279)(203,283)(204,287)(205,286)(206,285)(207,284)(208,288)(209,292)
(210,291)(211,290)(212,289)(213,293)(214,297)(215,296)(216,295)(217,294)
(218,298)(219,302)(220,301)(221,300)(222,299)(223,303)(224,307)(225,306)
(226,305)(227,304)(228,308)(229,312)(230,311)(231,310)(232,309)(233,313)
(234,317)(235,316)(236,315)(237,314)(238,318)(239,322)(240,321)(241,320)
(242,319);
s4 := Sym(322)!(  3,204)(  4,203)(  5,207)(  6,206)(  7,205)(  8,209)(  9,208)
( 10,212)( 11,211)( 12,210)( 13,214)( 14,213)( 15,217)( 16,216)( 17,215)
( 18,219)( 19,218)( 20,222)( 21,221)( 22,220)( 23,224)( 24,223)( 25,227)
( 26,226)( 27,225)( 28,229)( 29,228)( 30,232)( 31,231)( 32,230)( 33,234)
( 34,233)( 35,237)( 36,236)( 37,235)( 38,239)( 39,238)( 40,242)( 41,241)
( 42,240)( 43,164)( 44,163)( 45,167)( 46,166)( 47,165)( 48,169)( 49,168)
( 50,172)( 51,171)( 52,170)( 53,174)( 54,173)( 55,177)( 56,176)( 57,175)
( 58,179)( 59,178)( 60,182)( 61,181)( 62,180)( 63,184)( 64,183)( 65,187)
( 66,186)( 67,185)( 68,189)( 69,188)( 70,192)( 71,191)( 72,190)( 73,194)
( 74,193)( 75,197)( 76,196)( 77,195)( 78,199)( 79,198)( 80,202)( 81,201)
( 82,200)( 83,289)( 84,288)( 85,292)( 86,291)( 87,290)( 88,284)( 89,283)
( 90,287)( 91,286)( 92,285)( 93,299)( 94,298)( 95,302)( 96,301)( 97,300)
( 98,294)( 99,293)(100,297)(101,296)(102,295)(103,309)(104,308)(105,312)
(106,311)(107,310)(108,304)(109,303)(110,307)(111,306)(112,305)(113,319)
(114,318)(115,322)(116,321)(117,320)(118,314)(119,313)(120,317)(121,316)
(122,315)(123,249)(124,248)(125,252)(126,251)(127,250)(128,244)(129,243)
(130,247)(131,246)(132,245)(133,259)(134,258)(135,262)(136,261)(137,260)
(138,254)(139,253)(140,257)(141,256)(142,255)(143,269)(144,268)(145,272)
(146,271)(147,270)(148,264)(149,263)(150,267)(151,266)(152,265)(153,279)
(154,278)(155,282)(156,281)(157,280)(158,274)(159,273)(160,277)(161,276)
(162,275);
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*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope