Polytope of Type {2,10,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,8}*1280c
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}*640b
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 := ( 3,181)( 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*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,
s1*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s1*s2*s1*s3*s2*s3,
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)!( 3,195)( 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)!( 3,181)( 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*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,
s1*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s1*s2*s1*s3*s2*s3,
s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2*s3*s2*s1*s3 >;
to this polytope