Polytope of Type {2,20,16}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,20,16}*1280a
if this polytope has a name.
Group : SmallGroup(1280,323305)
Rank : 4
Schlafli Type : {2,20,16}
Number of vertices, edges, etc : 2, 20, 160, 16
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 : {2,20,8}*640a, {2,10,16}*640
4-fold quotients : {2,20,4}*320, {2,10,8}*320
5-fold quotients : {2,4,16}*256a
8-fold quotients : {2,20,2}*160, {2,10,4}*160
10-fold quotients : {2,4,8}*128a, {2,2,16}*128
16-fold quotients : {2,10,2}*80
20-fold quotients : {2,4,4}*64, {2,2,8}*64
32-fold quotients : {2,5,2}*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, 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);;
s2 := ( 3, 4)( 5, 7)( 8, 9)( 10, 12)( 13, 19)( 14, 18)( 15, 22)( 16, 21)
( 17, 20)( 23, 24)( 25, 27)( 28, 29)( 30, 32)( 33, 39)( 34, 38)( 35, 42)
( 36, 41)( 37, 40)( 43, 54)( 44, 53)( 45, 57)( 46, 56)( 47, 55)( 48, 59)
( 49, 58)( 50, 62)( 51, 61)( 52, 60)( 63, 74)( 64, 73)( 65, 77)( 66, 76)
( 67, 75)( 68, 79)( 69, 78)( 70, 82)( 71, 81)( 72, 80)( 83,104)( 84,103)
( 85,107)( 86,106)( 87,105)( 88,109)( 89,108)( 90,112)( 91,111)( 92,110)
( 93,119)( 94,118)( 95,122)( 96,121)( 97,120)( 98,114)( 99,113)(100,117)
(101,116)(102,115)(123,154)(124,153)(125,157)(126,156)(127,155)(128,159)
(129,158)(130,162)(131,161)(132,160)(133,144)(134,143)(135,147)(136,146)
(137,145)(138,149)(139,148)(140,152)(141,151)(142,150)(163,204)(164,203)
(165,207)(166,206)(167,205)(168,209)(169,208)(170,212)(171,211)(172,210)
(173,219)(174,218)(175,222)(176,221)(177,220)(178,214)(179,213)(180,217)
(181,216)(182,215)(183,224)(184,223)(185,227)(186,226)(187,225)(188,229)
(189,228)(190,232)(191,231)(192,230)(193,239)(194,238)(195,242)(196,241)
(197,240)(198,234)(199,233)(200,237)(201,236)(202,235)(243,304)(244,303)
(245,307)(246,306)(247,305)(248,309)(249,308)(250,312)(251,311)(252,310)
(253,319)(254,318)(255,322)(256,321)(257,320)(258,314)(259,313)(260,317)
(261,316)(262,315)(263,284)(264,283)(265,287)(266,286)(267,285)(268,289)
(269,288)(270,292)(271,291)(272,290)(273,299)(274,298)(275,302)(276,301)
(277,300)(278,294)(279,293)(280,297)(281,296)(282,295);;
s3 := ( 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);;
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, 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,
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, 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);
s2 := Sym(322)!( 3, 4)( 5, 7)( 8, 9)( 10, 12)( 13, 19)( 14, 18)( 15, 22)
( 16, 21)( 17, 20)( 23, 24)( 25, 27)( 28, 29)( 30, 32)( 33, 39)( 34, 38)
( 35, 42)( 36, 41)( 37, 40)( 43, 54)( 44, 53)( 45, 57)( 46, 56)( 47, 55)
( 48, 59)( 49, 58)( 50, 62)( 51, 61)( 52, 60)( 63, 74)( 64, 73)( 65, 77)
( 66, 76)( 67, 75)( 68, 79)( 69, 78)( 70, 82)( 71, 81)( 72, 80)( 83,104)
( 84,103)( 85,107)( 86,106)( 87,105)( 88,109)( 89,108)( 90,112)( 91,111)
( 92,110)( 93,119)( 94,118)( 95,122)( 96,121)( 97,120)( 98,114)( 99,113)
(100,117)(101,116)(102,115)(123,154)(124,153)(125,157)(126,156)(127,155)
(128,159)(129,158)(130,162)(131,161)(132,160)(133,144)(134,143)(135,147)
(136,146)(137,145)(138,149)(139,148)(140,152)(141,151)(142,150)(163,204)
(164,203)(165,207)(166,206)(167,205)(168,209)(169,208)(170,212)(171,211)
(172,210)(173,219)(174,218)(175,222)(176,221)(177,220)(178,214)(179,213)
(180,217)(181,216)(182,215)(183,224)(184,223)(185,227)(186,226)(187,225)
(188,229)(189,228)(190,232)(191,231)(192,230)(193,239)(194,238)(195,242)
(196,241)(197,240)(198,234)(199,233)(200,237)(201,236)(202,235)(243,304)
(244,303)(245,307)(246,306)(247,305)(248,309)(249,308)(250,312)(251,311)
(252,310)(253,319)(254,318)(255,322)(256,321)(257,320)(258,314)(259,313)
(260,317)(261,316)(262,315)(263,284)(264,283)(265,287)(266,286)(267,285)
(268,289)(269,288)(270,292)(271,291)(272,290)(273,299)(274,298)(275,302)
(276,301)(277,300)(278,294)(279,293)(280,297)(281,296)(282,295);
s3 := 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);
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,
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,
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 >;
to this polytope