Polytope of Type {2,10,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,8}*1280a
if this polytope has a name.
Group : SmallGroup(1280,1116450)
Rank : 4
Schlafli Type : {2,10,8}
Number of vertices, edges, etc : 2, 40, 160, 32
Order of s0s1s2s3 : 10
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-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}*640b, {2,10,4}*640a
4-fold quotients : {2,5,4}*320
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 := ( 3,195)( 4,196)( 5,217)( 6,218)( 7,219)( 8,220)( 9,209)( 10,210)
( 11,204)( 12,203)( 13,225)( 14,226)( 15,212)( 16,211)( 17,201)( 18,202)
( 19,208)( 20,207)( 21,221)( 22,222)( 23,216)( 24,215)( 25,197)( 26,198)
( 27,199)( 28,200)( 29,213)( 30,214)( 31,223)( 32,224)( 33,205)( 34,206)
( 35,163)( 36,164)( 37,185)( 38,186)( 39,187)( 40,188)( 41,177)( 42,178)
( 43,172)( 44,171)( 45,193)( 46,194)( 47,180)( 48,179)( 49,169)( 50,170)
( 51,176)( 52,175)( 53,189)( 54,190)( 55,184)( 56,183)( 57,165)( 58,166)
( 59,167)( 60,168)( 61,181)( 62,182)( 63,191)( 64,192)( 65,173)( 66,174)
( 67,291)( 68,292)( 69,313)( 70,314)( 71,315)( 72,316)( 73,305)( 74,306)
( 75,300)( 76,299)( 77,321)( 78,322)( 79,308)( 80,307)( 81,297)( 82,298)
( 83,304)( 84,303)( 85,317)( 86,318)( 87,312)( 88,311)( 89,293)( 90,294)
( 91,295)( 92,296)( 93,309)( 94,310)( 95,319)( 96,320)( 97,301)( 98,302)
( 99,259)(100,260)(101,281)(102,282)(103,283)(104,284)(105,273)(106,274)
(107,268)(108,267)(109,289)(110,290)(111,276)(112,275)(113,265)(114,266)
(115,272)(116,271)(117,285)(118,286)(119,280)(120,279)(121,261)(122,262)
(123,263)(124,264)(125,277)(126,278)(127,287)(128,288)(129,269)(130,270)
(131,227)(132,228)(133,249)(134,250)(135,251)(136,252)(137,241)(138,242)
(139,236)(140,235)(141,257)(142,258)(143,244)(144,243)(145,233)(146,234)
(147,240)(148,239)(149,253)(150,254)(151,248)(152,247)(153,229)(154,230)
(155,231)(156,232)(157,245)(158,246)(159,255)(160,256)(161,237)(162,238);;
s3 := ( 3, 21)( 4, 22)( 5, 20)( 6, 19)( 7, 26)( 8, 25)( 9, 23)( 10, 24)
( 11, 30)( 12, 29)( 13, 27)( 14, 28)( 15, 33)( 16, 34)( 17, 32)( 18, 31)
( 35, 53)( 36, 54)( 37, 52)( 38, 51)( 39, 58)( 40, 57)( 41, 55)( 42, 56)
( 43, 62)( 44, 61)( 45, 59)( 46, 60)( 47, 65)( 48, 66)( 49, 64)( 50, 63)
( 67, 85)( 68, 86)( 69, 84)( 70, 83)( 71, 90)( 72, 89)( 73, 87)( 74, 88)
( 75, 94)( 76, 93)( 77, 91)( 78, 92)( 79, 97)( 80, 98)( 81, 96)( 82, 95)
( 99,117)(100,118)(101,116)(102,115)(103,122)(104,121)(105,119)(106,120)
(107,126)(108,125)(109,123)(110,124)(111,129)(112,130)(113,128)(114,127)
(131,149)(132,150)(133,148)(134,147)(135,154)(136,153)(137,151)(138,152)
(139,158)(140,157)(141,155)(142,156)(143,161)(144,162)(145,160)(146,159)
(163,181)(164,182)(165,180)(166,179)(167,186)(168,185)(169,183)(170,184)
(171,190)(172,189)(173,187)(174,188)(175,193)(176,194)(177,192)(178,191)
(195,213)(196,214)(197,212)(198,211)(199,218)(200,217)(201,215)(202,216)
(203,222)(204,221)(205,219)(206,220)(207,225)(208,226)(209,224)(210,223)
(227,245)(228,246)(229,244)(230,243)(231,250)(232,249)(233,247)(234,248)
(235,254)(236,253)(237,251)(238,252)(239,257)(240,258)(241,256)(242,255)
(259,277)(260,278)(261,276)(262,275)(263,282)(264,281)(265,279)(266,280)
(267,286)(268,285)(269,283)(270,284)(271,289)(272,290)(273,288)(274,287)
(291,309)(292,310)(293,308)(294,307)(295,314)(296,313)(297,311)(298,312)
(299,318)(300,317)(301,315)(302,316)(303,321)(304,322)(305,320)(306,319);;
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*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2*s3*s2*s1*s3,
s3*s1*s2*s1*s3*s2*s1*s2*s3*s2*s3*s1*s2*s1*s2*s1*s2*s3*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)!( 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)!( 3,195)( 4,196)( 5,217)( 6,218)( 7,219)( 8,220)( 9,209)
( 10,210)( 11,204)( 12,203)( 13,225)( 14,226)( 15,212)( 16,211)( 17,201)
( 18,202)( 19,208)( 20,207)( 21,221)( 22,222)( 23,216)( 24,215)( 25,197)
( 26,198)( 27,199)( 28,200)( 29,213)( 30,214)( 31,223)( 32,224)( 33,205)
( 34,206)( 35,163)( 36,164)( 37,185)( 38,186)( 39,187)( 40,188)( 41,177)
( 42,178)( 43,172)( 44,171)( 45,193)( 46,194)( 47,180)( 48,179)( 49,169)
( 50,170)( 51,176)( 52,175)( 53,189)( 54,190)( 55,184)( 56,183)( 57,165)
( 58,166)( 59,167)( 60,168)( 61,181)( 62,182)( 63,191)( 64,192)( 65,173)
( 66,174)( 67,291)( 68,292)( 69,313)( 70,314)( 71,315)( 72,316)( 73,305)
( 74,306)( 75,300)( 76,299)( 77,321)( 78,322)( 79,308)( 80,307)( 81,297)
( 82,298)( 83,304)( 84,303)( 85,317)( 86,318)( 87,312)( 88,311)( 89,293)
( 90,294)( 91,295)( 92,296)( 93,309)( 94,310)( 95,319)( 96,320)( 97,301)
( 98,302)( 99,259)(100,260)(101,281)(102,282)(103,283)(104,284)(105,273)
(106,274)(107,268)(108,267)(109,289)(110,290)(111,276)(112,275)(113,265)
(114,266)(115,272)(116,271)(117,285)(118,286)(119,280)(120,279)(121,261)
(122,262)(123,263)(124,264)(125,277)(126,278)(127,287)(128,288)(129,269)
(130,270)(131,227)(132,228)(133,249)(134,250)(135,251)(136,252)(137,241)
(138,242)(139,236)(140,235)(141,257)(142,258)(143,244)(144,243)(145,233)
(146,234)(147,240)(148,239)(149,253)(150,254)(151,248)(152,247)(153,229)
(154,230)(155,231)(156,232)(157,245)(158,246)(159,255)(160,256)(161,237)
(162,238);
s3 := Sym(322)!( 3, 21)( 4, 22)( 5, 20)( 6, 19)( 7, 26)( 8, 25)( 9, 23)
( 10, 24)( 11, 30)( 12, 29)( 13, 27)( 14, 28)( 15, 33)( 16, 34)( 17, 32)
( 18, 31)( 35, 53)( 36, 54)( 37, 52)( 38, 51)( 39, 58)( 40, 57)( 41, 55)
( 42, 56)( 43, 62)( 44, 61)( 45, 59)( 46, 60)( 47, 65)( 48, 66)( 49, 64)
( 50, 63)( 67, 85)( 68, 86)( 69, 84)( 70, 83)( 71, 90)( 72, 89)( 73, 87)
( 74, 88)( 75, 94)( 76, 93)( 77, 91)( 78, 92)( 79, 97)( 80, 98)( 81, 96)
( 82, 95)( 99,117)(100,118)(101,116)(102,115)(103,122)(104,121)(105,119)
(106,120)(107,126)(108,125)(109,123)(110,124)(111,129)(112,130)(113,128)
(114,127)(131,149)(132,150)(133,148)(134,147)(135,154)(136,153)(137,151)
(138,152)(139,158)(140,157)(141,155)(142,156)(143,161)(144,162)(145,160)
(146,159)(163,181)(164,182)(165,180)(166,179)(167,186)(168,185)(169,183)
(170,184)(171,190)(172,189)(173,187)(174,188)(175,193)(176,194)(177,192)
(178,191)(195,213)(196,214)(197,212)(198,211)(199,218)(200,217)(201,215)
(202,216)(203,222)(204,221)(205,219)(206,220)(207,225)(208,226)(209,224)
(210,223)(227,245)(228,246)(229,244)(230,243)(231,250)(232,249)(233,247)
(234,248)(235,254)(236,253)(237,251)(238,252)(239,257)(240,258)(241,256)
(242,255)(259,277)(260,278)(261,276)(262,275)(263,282)(264,281)(265,279)
(266,280)(267,286)(268,285)(269,283)(270,284)(271,289)(272,290)(273,288)
(274,287)(291,309)(292,310)(293,308)(294,307)(295,314)(296,313)(297,311)
(298,312)(299,318)(300,317)(301,315)(302,316)(303,321)(304,322)(305,320)
(306,319);
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*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2*s3*s2*s1*s3,
s3*s1*s2*s1*s3*s2*s1*s2*s3*s2*s3*s1*s2*s1*s2*s1*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope