Polytope of Type {2,16,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,16,20}*1280a
if this polytope has a name.
Group : SmallGroup(1280,323305)
Rank : 4
Schlafli Type : {2,16,20}
Number of vertices, edges, etc : 2, 16, 160, 20
Order of s₀s₁s₂s₃ : 80
Order of s₀s₁s₂s₃s₂s₁ : 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 : {2,8,20}*640a, {2,16,10}*640
   4-fold quotients : {2,4,20}*320, {2,8,10}*320
   5-fold quotients : {2,16,4}*256a
   8-fold quotients : {2,2,20}*160, {2,4,10}*160
   10-fold quotients : {2,8,4}*128a, {2,16,2}*128
   16-fold quotients : {2,2,10}*80
   20-fold quotients : {2,4,4}*64, {2,8,2}*64
   32-fold quotients : {2,2,5}*40
   40-fold quotients : {2,2,4}*32, {2,4,2}*32
   80-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

to this polytope