Polytope of Type {2,4,80}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,80}*1280a
if this polytope has a name.
Group : SmallGroup(1280,323306)
Rank : 4
Schlafli Type : {2,4,80}
Number of vertices, edges, etc : 2, 4, 160, 80
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 : {2,4,40}*640a, {2,2,80}*640
4-fold quotients : {2,4,20}*320, {2,2,40}*320
5-fold quotients : {2,4,16}*256a
8-fold quotients : {2,2,20}*160, {2,4,10}*160
10-fold quotients : {2,4,8}*128a, {2,2,16}*128
16-fold quotients : {2,2,10}*80
20-fold quotients : {2,4,4}*64, {2,2,8}*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, 83)( 4, 84)( 5, 85)( 6, 86)( 7, 87)( 8, 88)( 9, 89)( 10, 90)
( 11, 91)( 12, 92)( 13, 93)( 14, 94)( 15, 95)( 16, 96)( 17, 97)( 18, 98)
( 19, 99)( 20,100)( 21,101)( 22,102)( 23,103)( 24,104)( 25,105)( 26,106)
( 27,107)( 28,108)( 29,109)( 30,110)( 31,111)( 32,112)( 33,113)( 34,114)
( 35,115)( 36,116)( 37,117)( 38,118)( 39,119)( 40,120)( 41,121)( 42,122)
( 43,123)( 44,124)( 45,125)( 46,126)( 47,127)( 48,128)( 49,129)( 50,130)
( 51,131)( 52,132)( 53,133)( 54,134)( 55,135)( 56,136)( 57,137)( 58,138)
( 59,139)( 60,140)( 61,141)( 62,142)( 63,143)( 64,144)( 65,145)( 66,146)
( 67,147)( 68,148)( 69,149)( 70,150)( 71,151)( 72,152)( 73,153)( 74,154)
( 75,155)( 76,156)( 77,157)( 78,158)( 79,159)( 80,160)( 81,161)( 82,162)
(163,243)(164,244)(165,245)(166,246)(167,247)(168,248)(169,249)(170,250)
(171,251)(172,252)(173,253)(174,254)(175,255)(176,256)(177,257)(178,258)
(179,259)(180,260)(181,261)(182,262)(183,263)(184,264)(185,265)(186,266)
(187,267)(188,268)(189,269)(190,270)(191,271)(192,272)(193,273)(194,274)
(195,275)(196,276)(197,277)(198,278)(199,279)(200,280)(201,281)(202,282)
(203,283)(204,284)(205,285)(206,286)(207,287)(208,288)(209,289)(210,290)
(211,291)(212,292)(213,293)(214,294)(215,295)(216,296)(217,297)(218,298)
(219,299)(220,300)(221,301)(222,302)(223,303)(224,304)(225,305)(226,306)
(227,307)(228,308)(229,309)(230,310)(231,311)(232,312)(233,313)(234,314)
(235,315)(236,316)(237,317)(238,318)(239,319)(240,320)(241,321)(242,322);;
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 := ( 3,164)( 4,163)( 5,167)( 6,166)( 7,165)( 8,169)( 9,168)( 10,172)
( 11,171)( 12,170)( 13,179)( 14,178)( 15,182)( 16,181)( 17,180)( 18,174)
( 19,173)( 20,177)( 21,176)( 22,175)( 23,184)( 24,183)( 25,187)( 26,186)
( 27,185)( 28,189)( 29,188)( 30,192)( 31,191)( 32,190)( 33,199)( 34,198)
( 35,202)( 36,201)( 37,200)( 38,194)( 39,193)( 40,197)( 41,196)( 42,195)
( 43,214)( 44,213)( 45,217)( 46,216)( 47,215)( 48,219)( 49,218)( 50,222)
( 51,221)( 52,220)( 53,204)( 54,203)( 55,207)( 56,206)( 57,205)( 58,209)
( 59,208)( 60,212)( 61,211)( 62,210)( 63,234)( 64,233)( 65,237)( 66,236)
( 67,235)( 68,239)( 69,238)( 70,242)( 71,241)( 72,240)( 73,224)( 74,223)
( 75,227)( 76,226)( 77,225)( 78,229)( 79,228)( 80,232)( 81,231)( 82,230)
( 83,244)( 84,243)( 85,247)( 86,246)( 87,245)( 88,249)( 89,248)( 90,252)
( 91,251)( 92,250)( 93,259)( 94,258)( 95,262)( 96,261)( 97,260)( 98,254)
( 99,253)(100,257)(101,256)(102,255)(103,264)(104,263)(105,267)(106,266)
(107,265)(108,269)(109,268)(110,272)(111,271)(112,270)(113,279)(114,278)
(115,282)(116,281)(117,280)(118,274)(119,273)(120,277)(121,276)(122,275)
(123,294)(124,293)(125,297)(126,296)(127,295)(128,299)(129,298)(130,302)
(131,301)(132,300)(133,284)(134,283)(135,287)(136,286)(137,285)(138,289)
(139,288)(140,292)(141,291)(142,290)(143,314)(144,313)(145,317)(146,316)
(147,315)(148,319)(149,318)(150,322)(151,321)(152,320)(153,304)(154,303)
(155,307)(156,306)(157,305)(158,309)(159,308)(160,312)(161,311)(162,310);;
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*s1*s2*s1*s2*s1*s2, 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*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*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*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*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(322)!(1,2);
s1 := Sym(322)!( 3, 83)( 4, 84)( 5, 85)( 6, 86)( 7, 87)( 8, 88)( 9, 89)
( 10, 90)( 11, 91)( 12, 92)( 13, 93)( 14, 94)( 15, 95)( 16, 96)( 17, 97)
( 18, 98)( 19, 99)( 20,100)( 21,101)( 22,102)( 23,103)( 24,104)( 25,105)
( 26,106)( 27,107)( 28,108)( 29,109)( 30,110)( 31,111)( 32,112)( 33,113)
( 34,114)( 35,115)( 36,116)( 37,117)( 38,118)( 39,119)( 40,120)( 41,121)
( 42,122)( 43,123)( 44,124)( 45,125)( 46,126)( 47,127)( 48,128)( 49,129)
( 50,130)( 51,131)( 52,132)( 53,133)( 54,134)( 55,135)( 56,136)( 57,137)
( 58,138)( 59,139)( 60,140)( 61,141)( 62,142)( 63,143)( 64,144)( 65,145)
( 66,146)( 67,147)( 68,148)( 69,149)( 70,150)( 71,151)( 72,152)( 73,153)
( 74,154)( 75,155)( 76,156)( 77,157)( 78,158)( 79,159)( 80,160)( 81,161)
( 82,162)(163,243)(164,244)(165,245)(166,246)(167,247)(168,248)(169,249)
(170,250)(171,251)(172,252)(173,253)(174,254)(175,255)(176,256)(177,257)
(178,258)(179,259)(180,260)(181,261)(182,262)(183,263)(184,264)(185,265)
(186,266)(187,267)(188,268)(189,269)(190,270)(191,271)(192,272)(193,273)
(194,274)(195,275)(196,276)(197,277)(198,278)(199,279)(200,280)(201,281)
(202,282)(203,283)(204,284)(205,285)(206,286)(207,287)(208,288)(209,289)
(210,290)(211,291)(212,292)(213,293)(214,294)(215,295)(216,296)(217,297)
(218,298)(219,299)(220,300)(221,301)(222,302)(223,303)(224,304)(225,305)
(226,306)(227,307)(228,308)(229,309)(230,310)(231,311)(232,312)(233,313)
(234,314)(235,315)(236,316)(237,317)(238,318)(239,319)(240,320)(241,321)
(242,322);
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)!( 3,164)( 4,163)( 5,167)( 6,166)( 7,165)( 8,169)( 9,168)
( 10,172)( 11,171)( 12,170)( 13,179)( 14,178)( 15,182)( 16,181)( 17,180)
( 18,174)( 19,173)( 20,177)( 21,176)( 22,175)( 23,184)( 24,183)( 25,187)
( 26,186)( 27,185)( 28,189)( 29,188)( 30,192)( 31,191)( 32,190)( 33,199)
( 34,198)( 35,202)( 36,201)( 37,200)( 38,194)( 39,193)( 40,197)( 41,196)
( 42,195)( 43,214)( 44,213)( 45,217)( 46,216)( 47,215)( 48,219)( 49,218)
( 50,222)( 51,221)( 52,220)( 53,204)( 54,203)( 55,207)( 56,206)( 57,205)
( 58,209)( 59,208)( 60,212)( 61,211)( 62,210)( 63,234)( 64,233)( 65,237)
( 66,236)( 67,235)( 68,239)( 69,238)( 70,242)( 71,241)( 72,240)( 73,224)
( 74,223)( 75,227)( 76,226)( 77,225)( 78,229)( 79,228)( 80,232)( 81,231)
( 82,230)( 83,244)( 84,243)( 85,247)( 86,246)( 87,245)( 88,249)( 89,248)
( 90,252)( 91,251)( 92,250)( 93,259)( 94,258)( 95,262)( 96,261)( 97,260)
( 98,254)( 99,253)(100,257)(101,256)(102,255)(103,264)(104,263)(105,267)
(106,266)(107,265)(108,269)(109,268)(110,272)(111,271)(112,270)(113,279)
(114,278)(115,282)(116,281)(117,280)(118,274)(119,273)(120,277)(121,276)
(122,275)(123,294)(124,293)(125,297)(126,296)(127,295)(128,299)(129,298)
(130,302)(131,301)(132,300)(133,284)(134,283)(135,287)(136,286)(137,285)
(138,289)(139,288)(140,292)(141,291)(142,290)(143,314)(144,313)(145,317)
(146,316)(147,315)(148,319)(149,318)(150,322)(151,321)(152,320)(153,304)
(154,303)(155,307)(156,306)(157,305)(158,309)(159,308)(160,312)(161,311)
(162,310);
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*s1*s2*s1*s2*s1*s2,
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*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*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*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*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope