Polytope of Type {2,5,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,5,8}*1280a
if this polytope has a name.
Group : SmallGroup(1280,1116450)
Rank : 4
Schlafli Type : {2,5,8}
Number of vertices, edges, etc : 2, 40, 160, 64
Order of s0s1s2s3 : 10
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 : {2,5,8}*640a, {2,5,8}*640b, {2,5,4}*640
4-fold quotients : {2,5,4}*320
32-fold quotients : {2,5,2}*40
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 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)(165,190)(166,189)
(167,177)(168,178)(169,183)(170,184)(171,180)(172,179)(173,174)(175,194)
(176,193)(185,191)(186,192)(187,188)(195,291)(196,292)(197,318)(198,317)
(199,305)(200,306)(201,311)(202,312)(203,308)(204,307)(205,302)(206,301)
(207,322)(208,321)(209,295)(210,296)(211,300)(212,299)(213,309)(214,310)
(215,297)(216,298)(217,319)(218,320)(219,316)(220,315)(221,294)(222,293)
(223,313)(224,314)(225,304)(226,303)(227,259)(228,260)(229,286)(230,285)
(231,273)(232,274)(233,279)(234,280)(235,276)(236,275)(237,270)(238,269)
(239,290)(240,289)(241,263)(242,264)(243,268)(244,267)(245,277)(246,278)
(247,265)(248,266)(249,287)(250,288)(251,284)(252,283)(253,262)(254,261)
(255,281)(256,282)(257,272)(258,271);;
s2 := ( 3, 35)( 4, 36)( 5, 57)( 6, 58)( 7, 59)( 8, 60)( 9, 49)( 10, 50)
( 11, 44)( 12, 43)( 13, 65)( 14, 66)( 15, 52)( 16, 51)( 17, 41)( 18, 42)
( 19, 48)( 20, 47)( 21, 61)( 22, 62)( 23, 56)( 24, 55)( 25, 37)( 26, 38)
( 27, 39)( 28, 40)( 29, 53)( 30, 54)( 31, 63)( 32, 64)( 33, 45)( 34, 46)
( 67,131)( 68,132)( 69,153)( 70,154)( 71,155)( 72,156)( 73,145)( 74,146)
( 75,140)( 76,139)( 77,161)( 78,162)( 79,148)( 80,147)( 81,137)( 82,138)
( 83,144)( 84,143)( 85,157)( 86,158)( 87,152)( 88,151)( 89,133)( 90,134)
( 91,135)( 92,136)( 93,149)( 94,150)( 95,159)( 96,160)( 97,141)( 98,142)
(101,121)(102,122)(103,123)(104,124)(105,113)(106,114)(107,108)(109,129)
(110,130)(111,116)(112,115)(117,125)(118,126)(119,120)(163,195)(164,196)
(165,217)(166,218)(167,219)(168,220)(169,209)(170,210)(171,204)(172,203)
(173,225)(174,226)(175,212)(176,211)(177,201)(178,202)(179,208)(180,207)
(181,221)(182,222)(183,216)(184,215)(185,197)(186,198)(187,199)(188,200)
(189,213)(190,214)(191,223)(192,224)(193,205)(194,206)(227,291)(228,292)
(229,313)(230,314)(231,315)(232,316)(233,305)(234,306)(235,300)(236,299)
(237,321)(238,322)(239,308)(240,307)(241,297)(242,298)(243,304)(244,303)
(245,317)(246,318)(247,312)(248,311)(249,293)(250,294)(251,295)(252,296)
(253,309)(254,310)(255,319)(256,320)(257,301)(258,302)(261,281)(262,282)
(263,283)(264,284)(265,273)(266,274)(267,268)(269,289)(270,290)(271,276)
(272,275)(277,285)(278,286)(279,280);;
s3 := ( 3,181)( 4,182)( 5,180)( 6,179)( 7,186)( 8,185)( 9,183)( 10,184)
( 11,190)( 12,189)( 13,187)( 14,188)( 15,193)( 16,194)( 17,192)( 18,191)
( 19,166)( 20,165)( 21,163)( 22,164)( 23,169)( 24,170)( 25,168)( 26,167)
( 27,173)( 28,174)( 29,172)( 30,171)( 31,178)( 32,177)( 33,175)( 34,176)
( 35,213)( 36,214)( 37,212)( 38,211)( 39,218)( 40,217)( 41,215)( 42,216)
( 43,222)( 44,221)( 45,219)( 46,220)( 47,225)( 48,226)( 49,224)( 50,223)
( 51,198)( 52,197)( 53,195)( 54,196)( 55,201)( 56,202)( 57,200)( 58,199)
( 59,205)( 60,206)( 61,204)( 62,203)( 63,210)( 64,209)( 65,207)( 66,208)
( 67,245)( 68,246)( 69,244)( 70,243)( 71,250)( 72,249)( 73,247)( 74,248)
( 75,254)( 76,253)( 77,251)( 78,252)( 79,257)( 80,258)( 81,256)( 82,255)
( 83,230)( 84,229)( 85,227)( 86,228)( 87,233)( 88,234)( 89,232)( 90,231)
( 91,237)( 92,238)( 93,236)( 94,235)( 95,242)( 96,241)( 97,239)( 98,240)
( 99,277)(100,278)(101,276)(102,275)(103,282)(104,281)(105,279)(106,280)
(107,286)(108,285)(109,283)(110,284)(111,289)(112,290)(113,288)(114,287)
(115,262)(116,261)(117,259)(118,260)(119,265)(120,266)(121,264)(122,263)
(123,269)(124,270)(125,268)(126,267)(127,274)(128,273)(129,271)(130,272)
(131,309)(132,310)(133,308)(134,307)(135,314)(136,313)(137,311)(138,312)
(139,318)(140,317)(141,315)(142,316)(143,321)(144,322)(145,320)(146,319)
(147,294)(148,293)(149,291)(150,292)(151,297)(152,298)(153,296)(154,295)
(155,301)(156,302)(157,300)(158,299)(159,306)(160,305)(161,303)(162,304);;
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, s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2,
s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2*s3*s2*s1*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(322)!(1,2);
s1 := 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)(165,190)
(166,189)(167,177)(168,178)(169,183)(170,184)(171,180)(172,179)(173,174)
(175,194)(176,193)(185,191)(186,192)(187,188)(195,291)(196,292)(197,318)
(198,317)(199,305)(200,306)(201,311)(202,312)(203,308)(204,307)(205,302)
(206,301)(207,322)(208,321)(209,295)(210,296)(211,300)(212,299)(213,309)
(214,310)(215,297)(216,298)(217,319)(218,320)(219,316)(220,315)(221,294)
(222,293)(223,313)(224,314)(225,304)(226,303)(227,259)(228,260)(229,286)
(230,285)(231,273)(232,274)(233,279)(234,280)(235,276)(236,275)(237,270)
(238,269)(239,290)(240,289)(241,263)(242,264)(243,268)(244,267)(245,277)
(246,278)(247,265)(248,266)(249,287)(250,288)(251,284)(252,283)(253,262)
(254,261)(255,281)(256,282)(257,272)(258,271);
s2 := Sym(322)!( 3, 35)( 4, 36)( 5, 57)( 6, 58)( 7, 59)( 8, 60)( 9, 49)
( 10, 50)( 11, 44)( 12, 43)( 13, 65)( 14, 66)( 15, 52)( 16, 51)( 17, 41)
( 18, 42)( 19, 48)( 20, 47)( 21, 61)( 22, 62)( 23, 56)( 24, 55)( 25, 37)
( 26, 38)( 27, 39)( 28, 40)( 29, 53)( 30, 54)( 31, 63)( 32, 64)( 33, 45)
( 34, 46)( 67,131)( 68,132)( 69,153)( 70,154)( 71,155)( 72,156)( 73,145)
( 74,146)( 75,140)( 76,139)( 77,161)( 78,162)( 79,148)( 80,147)( 81,137)
( 82,138)( 83,144)( 84,143)( 85,157)( 86,158)( 87,152)( 88,151)( 89,133)
( 90,134)( 91,135)( 92,136)( 93,149)( 94,150)( 95,159)( 96,160)( 97,141)
( 98,142)(101,121)(102,122)(103,123)(104,124)(105,113)(106,114)(107,108)
(109,129)(110,130)(111,116)(112,115)(117,125)(118,126)(119,120)(163,195)
(164,196)(165,217)(166,218)(167,219)(168,220)(169,209)(170,210)(171,204)
(172,203)(173,225)(174,226)(175,212)(176,211)(177,201)(178,202)(179,208)
(180,207)(181,221)(182,222)(183,216)(184,215)(185,197)(186,198)(187,199)
(188,200)(189,213)(190,214)(191,223)(192,224)(193,205)(194,206)(227,291)
(228,292)(229,313)(230,314)(231,315)(232,316)(233,305)(234,306)(235,300)
(236,299)(237,321)(238,322)(239,308)(240,307)(241,297)(242,298)(243,304)
(244,303)(245,317)(246,318)(247,312)(248,311)(249,293)(250,294)(251,295)
(252,296)(253,309)(254,310)(255,319)(256,320)(257,301)(258,302)(261,281)
(262,282)(263,283)(264,284)(265,273)(266,274)(267,268)(269,289)(270,290)
(271,276)(272,275)(277,285)(278,286)(279,280);
s3 := Sym(322)!( 3,181)( 4,182)( 5,180)( 6,179)( 7,186)( 8,185)( 9,183)
( 10,184)( 11,190)( 12,189)( 13,187)( 14,188)( 15,193)( 16,194)( 17,192)
( 18,191)( 19,166)( 20,165)( 21,163)( 22,164)( 23,169)( 24,170)( 25,168)
( 26,167)( 27,173)( 28,174)( 29,172)( 30,171)( 31,178)( 32,177)( 33,175)
( 34,176)( 35,213)( 36,214)( 37,212)( 38,211)( 39,218)( 40,217)( 41,215)
( 42,216)( 43,222)( 44,221)( 45,219)( 46,220)( 47,225)( 48,226)( 49,224)
( 50,223)( 51,198)( 52,197)( 53,195)( 54,196)( 55,201)( 56,202)( 57,200)
( 58,199)( 59,205)( 60,206)( 61,204)( 62,203)( 63,210)( 64,209)( 65,207)
( 66,208)( 67,245)( 68,246)( 69,244)( 70,243)( 71,250)( 72,249)( 73,247)
( 74,248)( 75,254)( 76,253)( 77,251)( 78,252)( 79,257)( 80,258)( 81,256)
( 82,255)( 83,230)( 84,229)( 85,227)( 86,228)( 87,233)( 88,234)( 89,232)
( 90,231)( 91,237)( 92,238)( 93,236)( 94,235)( 95,242)( 96,241)( 97,239)
( 98,240)( 99,277)(100,278)(101,276)(102,275)(103,282)(104,281)(105,279)
(106,280)(107,286)(108,285)(109,283)(110,284)(111,289)(112,290)(113,288)
(114,287)(115,262)(116,261)(117,259)(118,260)(119,265)(120,266)(121,264)
(122,263)(123,269)(124,270)(125,268)(126,267)(127,274)(128,273)(129,271)
(130,272)(131,309)(132,310)(133,308)(134,307)(135,314)(136,313)(137,311)
(138,312)(139,318)(140,317)(141,315)(142,316)(143,321)(144,322)(145,320)
(146,319)(147,294)(148,293)(149,291)(150,292)(151,297)(152,298)(153,296)
(154,295)(155,301)(156,302)(157,300)(158,299)(159,306)(160,305)(161,303)
(162,304);
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,
s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2,
s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2*s3*s2*s1*s3 >;
to this polytope