Polytope of Type {2,8,5}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,5}*1280b
if this polytope has a name.
Group : SmallGroup(1280,1116454)
Rank : 4
Schlafli Type : {2,8,5}
Number of vertices, edges, etc : 2, 64, 160, 40
Order of s0s1s2s3 : 20
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 : {2,4,5}*640
4-fold quotients : {2,4,5}*320
32-fold quotients : {2,2,5}*40
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3,179)( 4,180)( 5,182)( 6,181)( 7,184)( 8,183)( 9,185)( 10,186)
( 11,188)( 12,187)( 13,189)( 14,190)( 15,191)( 16,192)( 17,194)( 18,193)
( 19,164)( 20,163)( 21,165)( 22,166)( 23,167)( 24,168)( 25,170)( 26,169)
( 27,171)( 28,172)( 29,174)( 30,173)( 31,176)( 32,175)( 33,177)( 34,178)
( 35,211)( 36,212)( 37,214)( 38,213)( 39,216)( 40,215)( 41,217)( 42,218)
( 43,220)( 44,219)( 45,221)( 46,222)( 47,223)( 48,224)( 49,226)( 50,225)
( 51,196)( 52,195)( 53,197)( 54,198)( 55,199)( 56,200)( 57,202)( 58,201)
( 59,203)( 60,204)( 61,206)( 62,205)( 63,208)( 64,207)( 65,209)( 66,210)
( 67,243)( 68,244)( 69,246)( 70,245)( 71,248)( 72,247)( 73,249)( 74,250)
( 75,252)( 76,251)( 77,253)( 78,254)( 79,255)( 80,256)( 81,258)( 82,257)
( 83,228)( 84,227)( 85,229)( 86,230)( 87,231)( 88,232)( 89,234)( 90,233)
( 91,235)( 92,236)( 93,238)( 94,237)( 95,240)( 96,239)( 97,241)( 98,242)
( 99,275)(100,276)(101,278)(102,277)(103,280)(104,279)(105,281)(106,282)
(107,284)(108,283)(109,285)(110,286)(111,287)(112,288)(113,290)(114,289)
(115,260)(116,259)(117,261)(118,262)(119,263)(120,264)(121,266)(122,265)
(123,267)(124,268)(125,270)(126,269)(127,272)(128,271)(129,273)(130,274)
(131,307)(132,308)(133,310)(134,309)(135,312)(136,311)(137,313)(138,314)
(139,316)(140,315)(141,317)(142,318)(143,319)(144,320)(145,322)(146,321)
(147,292)(148,291)(149,293)(150,294)(151,295)(152,296)(153,298)(154,297)
(155,299)(156,300)(157,302)(158,301)(159,304)(160,303)(161,305)(162,306);;
s2 := ( 5, 30)( 6, 29)( 7, 17)( 8, 18)( 9, 23)( 10, 24)( 11, 20)( 12, 19)
( 13, 14)( 15, 34)( 16, 33)( 25, 31)( 26, 32)( 27, 28)( 35,131)( 36,132)
( 37,158)( 38,157)( 39,145)( 40,146)( 41,151)( 42,152)( 43,148)( 44,147)
( 45,142)( 46,141)( 47,162)( 48,161)( 49,135)( 50,136)( 51,140)( 52,139)
( 53,149)( 54,150)( 55,137)( 56,138)( 57,159)( 58,160)( 59,156)( 60,155)
( 61,134)( 62,133)( 63,153)( 64,154)( 65,144)( 66,143)( 67, 99)( 68,100)
( 69,126)( 70,125)( 71,113)( 72,114)( 73,119)( 74,120)( 75,116)( 76,115)
( 77,110)( 78,109)( 79,130)( 80,129)( 81,103)( 82,104)( 83,108)( 84,107)
( 85,117)( 86,118)( 87,105)( 88,106)( 89,127)( 90,128)( 91,124)( 92,123)
( 93,102)( 94,101)( 95,121)( 96,122)( 97,112)( 98,111)(163,164)(165,189)
(166,190)(167,178)(168,177)(169,184)(170,183)(171,179)(172,180)(175,193)
(176,194)(181,182)(185,192)(186,191)(195,292)(196,291)(197,317)(198,318)
(199,306)(200,305)(201,312)(202,311)(203,307)(204,308)(205,301)(206,302)
(207,321)(208,322)(209,296)(210,295)(211,299)(212,300)(213,310)(214,309)
(215,298)(216,297)(217,320)(218,319)(219,315)(220,316)(221,293)(222,294)
(223,314)(224,313)(225,303)(226,304)(227,260)(228,259)(229,285)(230,286)
(231,274)(232,273)(233,280)(234,279)(235,275)(236,276)(237,269)(238,270)
(239,289)(240,290)(241,264)(242,263)(243,267)(244,268)(245,278)(246,277)
(247,266)(248,265)(249,288)(250,287)(251,283)(252,284)(253,261)(254,262)
(255,282)(256,281)(257,271)(258,272);;
s3 := ( 3,131)( 4,132)( 5,150)( 6,149)( 7,151)( 8,152)( 9,138)( 10,137)
( 11,162)( 12,161)( 13,143)( 14,144)( 15,141)( 16,142)( 17,156)( 18,155)
( 19,148)( 20,147)( 21,134)( 22,133)( 23,135)( 24,136)( 25,153)( 26,154)
( 27,146)( 28,145)( 29,160)( 30,159)( 31,158)( 32,157)( 33,140)( 34,139)
( 35, 99)( 36,100)( 37,118)( 38,117)( 39,119)( 40,120)( 41,106)( 42,105)
( 43,130)( 44,129)( 45,111)( 46,112)( 47,109)( 48,110)( 49,124)( 50,123)
( 51,116)( 52,115)( 53,102)( 54,101)( 55,103)( 56,104)( 57,121)( 58,122)
( 59,114)( 60,113)( 61,128)( 62,127)( 63,126)( 64,125)( 65,108)( 66,107)
( 69, 86)( 70, 85)( 71, 87)( 72, 88)( 73, 74)( 75, 98)( 76, 97)( 77, 79)
( 78, 80)( 81, 92)( 82, 91)( 83, 84)( 93, 96)( 94, 95)(163,292)(164,291)
(165,309)(166,310)(167,312)(168,311)(169,297)(170,298)(171,321)(172,322)
(173,304)(174,303)(175,302)(176,301)(177,315)(178,316)(179,307)(180,308)
(181,293)(182,294)(183,296)(184,295)(185,314)(186,313)(187,305)(188,306)
(189,319)(190,320)(191,317)(192,318)(193,299)(194,300)(195,260)(196,259)
(197,277)(198,278)(199,280)(200,279)(201,265)(202,266)(203,289)(204,290)
(205,272)(206,271)(207,270)(208,269)(209,283)(210,284)(211,275)(212,276)
(213,261)(214,262)(215,264)(216,263)(217,282)(218,281)(219,273)(220,274)
(221,287)(222,288)(223,285)(224,286)(225,267)(226,268)(227,228)(229,245)
(230,246)(231,248)(232,247)(235,257)(236,258)(237,240)(238,239)(241,251)
(242,252)(249,250)(253,255)(254,256);;
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,
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*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(322)!(1,2);
s1 := Sym(322)!( 3,179)( 4,180)( 5,182)( 6,181)( 7,184)( 8,183)( 9,185)
( 10,186)( 11,188)( 12,187)( 13,189)( 14,190)( 15,191)( 16,192)( 17,194)
( 18,193)( 19,164)( 20,163)( 21,165)( 22,166)( 23,167)( 24,168)( 25,170)
( 26,169)( 27,171)( 28,172)( 29,174)( 30,173)( 31,176)( 32,175)( 33,177)
( 34,178)( 35,211)( 36,212)( 37,214)( 38,213)( 39,216)( 40,215)( 41,217)
( 42,218)( 43,220)( 44,219)( 45,221)( 46,222)( 47,223)( 48,224)( 49,226)
( 50,225)( 51,196)( 52,195)( 53,197)( 54,198)( 55,199)( 56,200)( 57,202)
( 58,201)( 59,203)( 60,204)( 61,206)( 62,205)( 63,208)( 64,207)( 65,209)
( 66,210)( 67,243)( 68,244)( 69,246)( 70,245)( 71,248)( 72,247)( 73,249)
( 74,250)( 75,252)( 76,251)( 77,253)( 78,254)( 79,255)( 80,256)( 81,258)
( 82,257)( 83,228)( 84,227)( 85,229)( 86,230)( 87,231)( 88,232)( 89,234)
( 90,233)( 91,235)( 92,236)( 93,238)( 94,237)( 95,240)( 96,239)( 97,241)
( 98,242)( 99,275)(100,276)(101,278)(102,277)(103,280)(104,279)(105,281)
(106,282)(107,284)(108,283)(109,285)(110,286)(111,287)(112,288)(113,290)
(114,289)(115,260)(116,259)(117,261)(118,262)(119,263)(120,264)(121,266)
(122,265)(123,267)(124,268)(125,270)(126,269)(127,272)(128,271)(129,273)
(130,274)(131,307)(132,308)(133,310)(134,309)(135,312)(136,311)(137,313)
(138,314)(139,316)(140,315)(141,317)(142,318)(143,319)(144,320)(145,322)
(146,321)(147,292)(148,291)(149,293)(150,294)(151,295)(152,296)(153,298)
(154,297)(155,299)(156,300)(157,302)(158,301)(159,304)(160,303)(161,305)
(162,306);
s2 := Sym(322)!( 5, 30)( 6, 29)( 7, 17)( 8, 18)( 9, 23)( 10, 24)( 11, 20)
( 12, 19)( 13, 14)( 15, 34)( 16, 33)( 25, 31)( 26, 32)( 27, 28)( 35,131)
( 36,132)( 37,158)( 38,157)( 39,145)( 40,146)( 41,151)( 42,152)( 43,148)
( 44,147)( 45,142)( 46,141)( 47,162)( 48,161)( 49,135)( 50,136)( 51,140)
( 52,139)( 53,149)( 54,150)( 55,137)( 56,138)( 57,159)( 58,160)( 59,156)
( 60,155)( 61,134)( 62,133)( 63,153)( 64,154)( 65,144)( 66,143)( 67, 99)
( 68,100)( 69,126)( 70,125)( 71,113)( 72,114)( 73,119)( 74,120)( 75,116)
( 76,115)( 77,110)( 78,109)( 79,130)( 80,129)( 81,103)( 82,104)( 83,108)
( 84,107)( 85,117)( 86,118)( 87,105)( 88,106)( 89,127)( 90,128)( 91,124)
( 92,123)( 93,102)( 94,101)( 95,121)( 96,122)( 97,112)( 98,111)(163,164)
(165,189)(166,190)(167,178)(168,177)(169,184)(170,183)(171,179)(172,180)
(175,193)(176,194)(181,182)(185,192)(186,191)(195,292)(196,291)(197,317)
(198,318)(199,306)(200,305)(201,312)(202,311)(203,307)(204,308)(205,301)
(206,302)(207,321)(208,322)(209,296)(210,295)(211,299)(212,300)(213,310)
(214,309)(215,298)(216,297)(217,320)(218,319)(219,315)(220,316)(221,293)
(222,294)(223,314)(224,313)(225,303)(226,304)(227,260)(228,259)(229,285)
(230,286)(231,274)(232,273)(233,280)(234,279)(235,275)(236,276)(237,269)
(238,270)(239,289)(240,290)(241,264)(242,263)(243,267)(244,268)(245,278)
(246,277)(247,266)(248,265)(249,288)(250,287)(251,283)(252,284)(253,261)
(254,262)(255,282)(256,281)(257,271)(258,272);
s3 := Sym(322)!( 3,131)( 4,132)( 5,150)( 6,149)( 7,151)( 8,152)( 9,138)
( 10,137)( 11,162)( 12,161)( 13,143)( 14,144)( 15,141)( 16,142)( 17,156)
( 18,155)( 19,148)( 20,147)( 21,134)( 22,133)( 23,135)( 24,136)( 25,153)
( 26,154)( 27,146)( 28,145)( 29,160)( 30,159)( 31,158)( 32,157)( 33,140)
( 34,139)( 35, 99)( 36,100)( 37,118)( 38,117)( 39,119)( 40,120)( 41,106)
( 42,105)( 43,130)( 44,129)( 45,111)( 46,112)( 47,109)( 48,110)( 49,124)
( 50,123)( 51,116)( 52,115)( 53,102)( 54,101)( 55,103)( 56,104)( 57,121)
( 58,122)( 59,114)( 60,113)( 61,128)( 62,127)( 63,126)( 64,125)( 65,108)
( 66,107)( 69, 86)( 70, 85)( 71, 87)( 72, 88)( 73, 74)( 75, 98)( 76, 97)
( 77, 79)( 78, 80)( 81, 92)( 82, 91)( 83, 84)( 93, 96)( 94, 95)(163,292)
(164,291)(165,309)(166,310)(167,312)(168,311)(169,297)(170,298)(171,321)
(172,322)(173,304)(174,303)(175,302)(176,301)(177,315)(178,316)(179,307)
(180,308)(181,293)(182,294)(183,296)(184,295)(185,314)(186,313)(187,305)
(188,306)(189,319)(190,320)(191,317)(192,318)(193,299)(194,300)(195,260)
(196,259)(197,277)(198,278)(199,280)(200,279)(201,265)(202,266)(203,289)
(204,290)(205,272)(206,271)(207,270)(208,269)(209,283)(210,284)(211,275)
(212,276)(213,261)(214,262)(215,264)(216,263)(217,282)(218,281)(219,273)
(220,274)(221,287)(222,288)(223,285)(224,286)(225,267)(226,268)(227,228)
(229,245)(230,246)(231,248)(232,247)(235,257)(236,258)(237,240)(238,239)
(241,251)(242,252)(249,250)(253,255)(254,256);
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, 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*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2 >;
to this polytope