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Polytope of Type {20,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,16}*640a
Also Known As : {20,16|2}. if this polytope has another name.
Group : SmallGroup(640,2066)
Rank : 3
Schlafli Type : {20,16}
Number of vertices, edges, etc : 20, 160, 16
Order of s0s1s2 : 80
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {20,16,2} of size 1280
Vertex Figure Of :
   {2,20,16} of size 1280
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {20,8}*320a, {10,16}*320
   4-fold quotients : {20,4}*160, {10,8}*160
   5-fold quotients : {4,16}*128a
   8-fold quotients : {20,2}*80, {10,4}*80
   10-fold quotients : {4,8}*64a, {2,16}*64
   16-fold quotients : {10,2}*40
   20-fold quotients : {4,4}*32, {2,8}*32
   32-fold quotients : {5,2}*20
   40-fold quotients : {2,4}*16, {4,2}*16
   80-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {20,16}*1280a, {40,16}*1280c, {40,16}*1280d, {20,32}*1280a, {20,32}*1280b
   3-fold covers : {60,16}*1920a, {20,48}*1920a
Permutation Representation (GAP) :
s0 := (  1, 81)(  2, 85)(  3, 84)(  4, 83)(  5, 82)(  6, 86)(  7, 90)(  8, 89)
(  9, 88)( 10, 87)( 11, 91)( 12, 95)( 13, 94)( 14, 93)( 15, 92)( 16, 96)
( 17,100)( 18, 99)( 19, 98)( 20, 97)( 21,101)( 22,105)( 23,104)( 24,103)
( 25,102)( 26,106)( 27,110)( 28,109)( 29,108)( 30,107)( 31,111)( 32,115)
( 33,114)( 34,113)( 35,112)( 36,116)( 37,120)( 38,119)( 39,118)( 40,117)
( 41,121)( 42,125)( 43,124)( 44,123)( 45,122)( 46,126)( 47,130)( 48,129)
( 49,128)( 50,127)( 51,131)( 52,135)( 53,134)( 54,133)( 55,132)( 56,136)
( 57,140)( 58,139)( 59,138)( 60,137)( 61,141)( 62,145)( 63,144)( 64,143)
( 65,142)( 66,146)( 67,150)( 68,149)( 69,148)( 70,147)( 71,151)( 72,155)
( 73,154)( 74,153)( 75,152)( 76,156)( 77,160)( 78,159)( 79,158)( 80,157)
(161,241)(162,245)(163,244)(164,243)(165,242)(166,246)(167,250)(168,249)
(169,248)(170,247)(171,251)(172,255)(173,254)(174,253)(175,252)(176,256)
(177,260)(178,259)(179,258)(180,257)(181,261)(182,265)(183,264)(184,263)
(185,262)(186,266)(187,270)(188,269)(189,268)(190,267)(191,271)(192,275)
(193,274)(194,273)(195,272)(196,276)(197,280)(198,279)(199,278)(200,277)
(201,281)(202,285)(203,284)(204,283)(205,282)(206,286)(207,290)(208,289)
(209,288)(210,287)(211,291)(212,295)(213,294)(214,293)(215,292)(216,296)
(217,300)(218,299)(219,298)(220,297)(221,301)(222,305)(223,304)(224,303)
(225,302)(226,306)(227,310)(228,309)(229,308)(230,307)(231,311)(232,315)
(233,314)(234,313)(235,312)(236,316)(237,320)(238,319)(239,318)(240,317);;
s1 := (  1,  2)(  3,  5)(  6,  7)(  8, 10)( 11, 17)( 12, 16)( 13, 20)( 14, 19)
( 15, 18)( 21, 22)( 23, 25)( 26, 27)( 28, 30)( 31, 37)( 32, 36)( 33, 40)
( 34, 39)( 35, 38)( 41, 52)( 42, 51)( 43, 55)( 44, 54)( 45, 53)( 46, 57)
( 47, 56)( 48, 60)( 49, 59)( 50, 58)( 61, 72)( 62, 71)( 63, 75)( 64, 74)
( 65, 73)( 66, 77)( 67, 76)( 68, 80)( 69, 79)( 70, 78)( 81,102)( 82,101)
( 83,105)( 84,104)( 85,103)( 86,107)( 87,106)( 88,110)( 89,109)( 90,108)
( 91,117)( 92,116)( 93,120)( 94,119)( 95,118)( 96,112)( 97,111)( 98,115)
( 99,114)(100,113)(121,152)(122,151)(123,155)(124,154)(125,153)(126,157)
(127,156)(128,160)(129,159)(130,158)(131,142)(132,141)(133,145)(134,144)
(135,143)(136,147)(137,146)(138,150)(139,149)(140,148)(161,202)(162,201)
(163,205)(164,204)(165,203)(166,207)(167,206)(168,210)(169,209)(170,208)
(171,217)(172,216)(173,220)(174,219)(175,218)(176,212)(177,211)(178,215)
(179,214)(180,213)(181,222)(182,221)(183,225)(184,224)(185,223)(186,227)
(187,226)(188,230)(189,229)(190,228)(191,237)(192,236)(193,240)(194,239)
(195,238)(196,232)(197,231)(198,235)(199,234)(200,233)(241,302)(242,301)
(243,305)(244,304)(245,303)(246,307)(247,306)(248,310)(249,309)(250,308)
(251,317)(252,316)(253,320)(254,319)(255,318)(256,312)(257,311)(258,315)
(259,314)(260,313)(261,282)(262,281)(263,285)(264,284)(265,283)(266,287)
(267,286)(268,290)(269,289)(270,288)(271,297)(272,296)(273,300)(274,299)
(275,298)(276,292)(277,291)(278,295)(279,294)(280,293);;
s2 := (  1,161)(  2,162)(  3,163)(  4,164)(  5,165)(  6,166)(  7,167)(  8,168)
(  9,169)( 10,170)( 11,176)( 12,177)( 13,178)( 14,179)( 15,180)( 16,171)
( 17,172)( 18,173)( 19,174)( 20,175)( 21,181)( 22,182)( 23,183)( 24,184)
( 25,185)( 26,186)( 27,187)( 28,188)( 29,189)( 30,190)( 31,196)( 32,197)
( 33,198)( 34,199)( 35,200)( 36,191)( 37,192)( 38,193)( 39,194)( 40,195)
( 41,211)( 42,212)( 43,213)( 44,214)( 45,215)( 46,216)( 47,217)( 48,218)
( 49,219)( 50,220)( 51,201)( 52,202)( 53,203)( 54,204)( 55,205)( 56,206)
( 57,207)( 58,208)( 59,209)( 60,210)( 61,231)( 62,232)( 63,233)( 64,234)
( 65,235)( 66,236)( 67,237)( 68,238)( 69,239)( 70,240)( 71,221)( 72,222)
( 73,223)( 74,224)( 75,225)( 76,226)( 77,227)( 78,228)( 79,229)( 80,230)
( 81,241)( 82,242)( 83,243)( 84,244)( 85,245)( 86,246)( 87,247)( 88,248)
( 89,249)( 90,250)( 91,256)( 92,257)( 93,258)( 94,259)( 95,260)( 96,251)
( 97,252)( 98,253)( 99,254)(100,255)(101,261)(102,262)(103,263)(104,264)
(105,265)(106,266)(107,267)(108,268)(109,269)(110,270)(111,276)(112,277)
(113,278)(114,279)(115,280)(116,271)(117,272)(118,273)(119,274)(120,275)
(121,291)(122,292)(123,293)(124,294)(125,295)(126,296)(127,297)(128,298)
(129,299)(130,300)(131,281)(132,282)(133,283)(134,284)(135,285)(136,286)
(137,287)(138,288)(139,289)(140,290)(141,311)(142,312)(143,313)(144,314)
(145,315)(146,316)(147,317)(148,318)(149,319)(150,320)(151,301)(152,302)
(153,303)(154,304)(155,305)(156,306)(157,307)(158,308)(159,309)(160,310);;
poly := Group([s0,s1,s2]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(320)!(  1, 81)(  2, 85)(  3, 84)(  4, 83)(  5, 82)(  6, 86)(  7, 90)
(  8, 89)(  9, 88)( 10, 87)( 11, 91)( 12, 95)( 13, 94)( 14, 93)( 15, 92)
( 16, 96)( 17,100)( 18, 99)( 19, 98)( 20, 97)( 21,101)( 22,105)( 23,104)
( 24,103)( 25,102)( 26,106)( 27,110)( 28,109)( 29,108)( 30,107)( 31,111)
( 32,115)( 33,114)( 34,113)( 35,112)( 36,116)( 37,120)( 38,119)( 39,118)
( 40,117)( 41,121)( 42,125)( 43,124)( 44,123)( 45,122)( 46,126)( 47,130)
( 48,129)( 49,128)( 50,127)( 51,131)( 52,135)( 53,134)( 54,133)( 55,132)
( 56,136)( 57,140)( 58,139)( 59,138)( 60,137)( 61,141)( 62,145)( 63,144)
( 64,143)( 65,142)( 66,146)( 67,150)( 68,149)( 69,148)( 70,147)( 71,151)
( 72,155)( 73,154)( 74,153)( 75,152)( 76,156)( 77,160)( 78,159)( 79,158)
( 80,157)(161,241)(162,245)(163,244)(164,243)(165,242)(166,246)(167,250)
(168,249)(169,248)(170,247)(171,251)(172,255)(173,254)(174,253)(175,252)
(176,256)(177,260)(178,259)(179,258)(180,257)(181,261)(182,265)(183,264)
(184,263)(185,262)(186,266)(187,270)(188,269)(189,268)(190,267)(191,271)
(192,275)(193,274)(194,273)(195,272)(196,276)(197,280)(198,279)(199,278)
(200,277)(201,281)(202,285)(203,284)(204,283)(205,282)(206,286)(207,290)
(208,289)(209,288)(210,287)(211,291)(212,295)(213,294)(214,293)(215,292)
(216,296)(217,300)(218,299)(219,298)(220,297)(221,301)(222,305)(223,304)
(224,303)(225,302)(226,306)(227,310)(228,309)(229,308)(230,307)(231,311)
(232,315)(233,314)(234,313)(235,312)(236,316)(237,320)(238,319)(239,318)
(240,317);
s1 := Sym(320)!(  1,  2)(  3,  5)(  6,  7)(  8, 10)( 11, 17)( 12, 16)( 13, 20)
( 14, 19)( 15, 18)( 21, 22)( 23, 25)( 26, 27)( 28, 30)( 31, 37)( 32, 36)
( 33, 40)( 34, 39)( 35, 38)( 41, 52)( 42, 51)( 43, 55)( 44, 54)( 45, 53)
( 46, 57)( 47, 56)( 48, 60)( 49, 59)( 50, 58)( 61, 72)( 62, 71)( 63, 75)
( 64, 74)( 65, 73)( 66, 77)( 67, 76)( 68, 80)( 69, 79)( 70, 78)( 81,102)
( 82,101)( 83,105)( 84,104)( 85,103)( 86,107)( 87,106)( 88,110)( 89,109)
( 90,108)( 91,117)( 92,116)( 93,120)( 94,119)( 95,118)( 96,112)( 97,111)
( 98,115)( 99,114)(100,113)(121,152)(122,151)(123,155)(124,154)(125,153)
(126,157)(127,156)(128,160)(129,159)(130,158)(131,142)(132,141)(133,145)
(134,144)(135,143)(136,147)(137,146)(138,150)(139,149)(140,148)(161,202)
(162,201)(163,205)(164,204)(165,203)(166,207)(167,206)(168,210)(169,209)
(170,208)(171,217)(172,216)(173,220)(174,219)(175,218)(176,212)(177,211)
(178,215)(179,214)(180,213)(181,222)(182,221)(183,225)(184,224)(185,223)
(186,227)(187,226)(188,230)(189,229)(190,228)(191,237)(192,236)(193,240)
(194,239)(195,238)(196,232)(197,231)(198,235)(199,234)(200,233)(241,302)
(242,301)(243,305)(244,304)(245,303)(246,307)(247,306)(248,310)(249,309)
(250,308)(251,317)(252,316)(253,320)(254,319)(255,318)(256,312)(257,311)
(258,315)(259,314)(260,313)(261,282)(262,281)(263,285)(264,284)(265,283)
(266,287)(267,286)(268,290)(269,289)(270,288)(271,297)(272,296)(273,300)
(274,299)(275,298)(276,292)(277,291)(278,295)(279,294)(280,293);
s2 := Sym(320)!(  1,161)(  2,162)(  3,163)(  4,164)(  5,165)(  6,166)(  7,167)
(  8,168)(  9,169)( 10,170)( 11,176)( 12,177)( 13,178)( 14,179)( 15,180)
( 16,171)( 17,172)( 18,173)( 19,174)( 20,175)( 21,181)( 22,182)( 23,183)
( 24,184)( 25,185)( 26,186)( 27,187)( 28,188)( 29,189)( 30,190)( 31,196)
( 32,197)( 33,198)( 34,199)( 35,200)( 36,191)( 37,192)( 38,193)( 39,194)
( 40,195)( 41,211)( 42,212)( 43,213)( 44,214)( 45,215)( 46,216)( 47,217)
( 48,218)( 49,219)( 50,220)( 51,201)( 52,202)( 53,203)( 54,204)( 55,205)
( 56,206)( 57,207)( 58,208)( 59,209)( 60,210)( 61,231)( 62,232)( 63,233)
( 64,234)( 65,235)( 66,236)( 67,237)( 68,238)( 69,239)( 70,240)( 71,221)
( 72,222)( 73,223)( 74,224)( 75,225)( 76,226)( 77,227)( 78,228)( 79,229)
( 80,230)( 81,241)( 82,242)( 83,243)( 84,244)( 85,245)( 86,246)( 87,247)
( 88,248)( 89,249)( 90,250)( 91,256)( 92,257)( 93,258)( 94,259)( 95,260)
( 96,251)( 97,252)( 98,253)( 99,254)(100,255)(101,261)(102,262)(103,263)
(104,264)(105,265)(106,266)(107,267)(108,268)(109,269)(110,270)(111,276)
(112,277)(113,278)(114,279)(115,280)(116,271)(117,272)(118,273)(119,274)
(120,275)(121,291)(122,292)(123,293)(124,294)(125,295)(126,296)(127,297)
(128,298)(129,299)(130,300)(131,281)(132,282)(133,283)(134,284)(135,285)
(136,286)(137,287)(138,288)(139,289)(140,290)(141,311)(142,312)(143,313)
(144,314)(145,315)(146,316)(147,317)(148,318)(149,319)(150,320)(151,301)
(152,302)(153,303)(154,304)(155,305)(156,306)(157,307)(158,308)(159,309)
(160,310);
poly := sub<Sym(320)|s0,s1,s2>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope