Polytope of Type {2,20,16}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,20,16}*1280b
if this polytope has a name.
Group : SmallGroup(1280,323453)
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
4-fold quotients : {2,20,4}*320, {2,10,8}*320
5-fold quotients : {2,4,16}*256b
8-fold quotients : {2,20,2}*160, {2,10,4}*160
10-fold quotients : {2,4,8}*128a
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)
( 43,128)( 44,132)( 45,131)( 46,130)( 47,129)( 48,123)( 49,127)( 50,126)
( 51,125)( 52,124)( 53,138)( 54,142)( 55,141)( 56,140)( 57,139)( 58,133)
( 59,137)( 60,136)( 61,135)( 62,134)( 63,148)( 64,152)( 65,151)( 66,150)
( 67,149)( 68,143)( 69,147)( 70,146)( 71,145)( 72,144)( 73,158)( 74,162)
( 75,161)( 76,160)( 77,159)( 78,153)( 79,157)( 80,156)( 81,155)( 82,154)
(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)
(203,288)(204,292)(205,291)(206,290)(207,289)(208,283)(209,287)(210,286)
(211,285)(212,284)(213,298)(214,302)(215,301)(216,300)(217,299)(218,293)
(219,297)(220,296)(221,295)(222,294)(223,308)(224,312)(225,311)(226,310)
(227,309)(228,303)(229,307)(230,306)(231,305)(232,304)(233,318)(234,322)
(235,321)(236,320)(237,319)(238,313)(239,317)(240,316)(241,315)(242,314);;
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)(243,309)(244,308)
(245,312)(246,311)(247,310)(248,304)(249,303)(250,307)(251,306)(252,305)
(253,314)(254,313)(255,317)(256,316)(257,315)(258,319)(259,318)(260,322)
(261,321)(262,320)(263,289)(264,288)(265,292)(266,291)(267,290)(268,284)
(269,283)(270,287)(271,286)(272,285)(273,294)(274,293)(275,297)(276,296)
(277,295)(278,299)(279,298)(280,302)(281,301)(282,300);;
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)( 23,188)( 24,189)( 25,190)( 26,191)
( 27,192)( 28,183)( 29,184)( 30,185)( 31,186)( 32,187)( 33,193)( 34,194)
( 35,195)( 36,196)( 37,197)( 38,198)( 39,199)( 40,200)( 41,201)( 42,202)
( 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)( 63,238)( 64,239)( 65,240)( 66,241)
( 67,242)( 68,233)( 69,234)( 70,235)( 71,236)( 72,237)( 73,228)( 74,229)
( 75,230)( 76,231)( 77,232)( 78,223)( 79,224)( 80,225)( 81,226)( 82,227)
( 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)(103,268)(104,269)(105,270)(106,271)
(107,272)(108,263)(109,264)(110,265)(111,266)(112,267)(113,273)(114,274)
(115,275)(116,276)(117,277)(118,278)(119,279)(120,280)(121,281)(122,282)
(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)(143,318)(144,319)(145,320)(146,321)
(147,322)(148,313)(149,314)(150,315)(151,316)(152,317)(153,308)(154,309)
(155,310)(156,311)(157,312)(158,303)(159,304)(160,305)(161,306)(162,307);;
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,
s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2,
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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*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)( 43,128)( 44,132)( 45,131)( 46,130)( 47,129)( 48,123)( 49,127)
( 50,126)( 51,125)( 52,124)( 53,138)( 54,142)( 55,141)( 56,140)( 57,139)
( 58,133)( 59,137)( 60,136)( 61,135)( 62,134)( 63,148)( 64,152)( 65,151)
( 66,150)( 67,149)( 68,143)( 69,147)( 70,146)( 71,145)( 72,144)( 73,158)
( 74,162)( 75,161)( 76,160)( 77,159)( 78,153)( 79,157)( 80,156)( 81,155)
( 82,154)(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)(203,288)(204,292)(205,291)(206,290)(207,289)(208,283)(209,287)
(210,286)(211,285)(212,284)(213,298)(214,302)(215,301)(216,300)(217,299)
(218,293)(219,297)(220,296)(221,295)(222,294)(223,308)(224,312)(225,311)
(226,310)(227,309)(228,303)(229,307)(230,306)(231,305)(232,304)(233,318)
(234,322)(235,321)(236,320)(237,319)(238,313)(239,317)(240,316)(241,315)
(242,314);
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)(243,309)
(244,308)(245,312)(246,311)(247,310)(248,304)(249,303)(250,307)(251,306)
(252,305)(253,314)(254,313)(255,317)(256,316)(257,315)(258,319)(259,318)
(260,322)(261,321)(262,320)(263,289)(264,288)(265,292)(266,291)(267,290)
(268,284)(269,283)(270,287)(271,286)(272,285)(273,294)(274,293)(275,297)
(276,296)(277,295)(278,299)(279,298)(280,302)(281,301)(282,300);
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)( 23,188)( 24,189)( 25,190)
( 26,191)( 27,192)( 28,183)( 29,184)( 30,185)( 31,186)( 32,187)( 33,193)
( 34,194)( 35,195)( 36,196)( 37,197)( 38,198)( 39,199)( 40,200)( 41,201)
( 42,202)( 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)( 63,238)( 64,239)( 65,240)
( 66,241)( 67,242)( 68,233)( 69,234)( 70,235)( 71,236)( 72,237)( 73,228)
( 74,229)( 75,230)( 76,231)( 77,232)( 78,223)( 79,224)( 80,225)( 81,226)
( 82,227)( 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)(103,268)(104,269)(105,270)
(106,271)(107,272)(108,263)(109,264)(110,265)(111,266)(112,267)(113,273)
(114,274)(115,275)(116,276)(117,277)(118,278)(119,279)(120,280)(121,281)
(122,282)(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)(143,318)(144,319)(145,320)
(146,321)(147,322)(148,313)(149,314)(150,315)(151,316)(152,317)(153,308)
(154,309)(155,310)(156,311)(157,312)(158,303)(159,304)(160,305)(161,306)
(162,307);
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, s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2,
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope