Polytope of Type {2,2,4,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,10}*1280b
if this polytope has a name.
Group : SmallGroup(1280,1116461)
Rank : 5
Schlafli Type : {2,2,4,10}
Number of vertices, edges, etc : 2, 2, 16, 80, 40
Order of s0s1s2s3s4 : 10
Order of s0s1s2s3s4s3s2s1 : 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 : {2,2,4,5}*640
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 5, 86)( 6, 85)( 7, 88)( 8, 87)( 9, 90)( 10, 89)( 11, 92)( 12, 91)
( 13, 94)( 14, 93)( 15, 96)( 16, 95)( 17, 98)( 18, 97)( 19,100)( 20, 99)
( 21,102)( 22,101)( 23,104)( 24,103)( 25,106)( 26,105)( 27,108)( 28,107)
( 29,110)( 30,109)( 31,112)( 32,111)( 33,114)( 34,113)( 35,116)( 36,115)
( 37,118)( 38,117)( 39,120)( 40,119)( 41,122)( 42,121)( 43,124)( 44,123)
( 45,126)( 46,125)( 47,128)( 48,127)( 49,130)( 50,129)( 51,132)( 52,131)
( 53,134)( 54,133)( 55,136)( 56,135)( 57,138)( 58,137)( 59,140)( 60,139)
( 61,142)( 62,141)( 63,144)( 64,143)( 65,146)( 66,145)( 67,148)( 68,147)
( 69,150)( 70,149)( 71,152)( 72,151)( 73,154)( 74,153)( 75,156)( 76,155)
( 77,158)( 78,157)( 79,160)( 80,159)( 81,162)( 82,161)( 83,164)( 84,163)
(165,246)(166,245)(167,248)(168,247)(169,250)(170,249)(171,252)(172,251)
(173,254)(174,253)(175,256)(176,255)(177,258)(178,257)(179,260)(180,259)
(181,262)(182,261)(183,264)(184,263)(185,266)(186,265)(187,268)(188,267)
(189,270)(190,269)(191,272)(192,271)(193,274)(194,273)(195,276)(196,275)
(197,278)(198,277)(199,280)(200,279)(201,282)(202,281)(203,284)(204,283)
(205,286)(206,285)(207,288)(208,287)(209,290)(210,289)(211,292)(212,291)
(213,294)(214,293)(215,296)(216,295)(217,298)(218,297)(219,300)(220,299)
(221,302)(222,301)(223,304)(224,303)(225,306)(226,305)(227,308)(228,307)
(229,310)(230,309)(231,312)(232,311)(233,314)(234,313)(235,316)(236,315)
(237,318)(238,317)(239,320)(240,319)(241,322)(242,321)(243,324)(244,323);;
s3 := ( 5,165)( 6,175)( 7,178)( 8,172)( 9,169)( 10,179)( 11,174)( 12,168)
( 13,177)( 14,171)( 15,166)( 16,176)( 17,173)( 18,167)( 19,170)( 20,180)
( 21,229)( 22,239)( 23,242)( 24,236)( 25,233)( 26,243)( 27,238)( 28,232)
( 29,241)( 30,235)( 31,230)( 32,240)( 33,237)( 34,231)( 35,234)( 36,244)
( 37,213)( 38,223)( 39,226)( 40,220)( 41,217)( 42,227)( 43,222)( 44,216)
( 45,225)( 46,219)( 47,214)( 48,224)( 49,221)( 50,215)( 51,218)( 52,228)
( 53,197)( 54,207)( 55,210)( 56,204)( 57,201)( 58,211)( 59,206)( 60,200)
( 61,209)( 62,203)( 63,198)( 64,208)( 65,205)( 66,199)( 67,202)( 68,212)
( 69,181)( 70,191)( 71,194)( 72,188)( 73,185)( 74,195)( 75,190)( 76,184)
( 77,193)( 78,187)( 79,182)( 80,192)( 81,189)( 82,183)( 83,186)( 84,196)
( 85,245)( 86,255)( 87,258)( 88,252)( 89,249)( 90,259)( 91,254)( 92,248)
( 93,257)( 94,251)( 95,246)( 96,256)( 97,253)( 98,247)( 99,250)(100,260)
(101,309)(102,319)(103,322)(104,316)(105,313)(106,323)(107,318)(108,312)
(109,321)(110,315)(111,310)(112,320)(113,317)(114,311)(115,314)(116,324)
(117,293)(118,303)(119,306)(120,300)(121,297)(122,307)(123,302)(124,296)
(125,305)(126,299)(127,294)(128,304)(129,301)(130,295)(131,298)(132,308)
(133,277)(134,287)(135,290)(136,284)(137,281)(138,291)(139,286)(140,280)
(141,289)(142,283)(143,278)(144,288)(145,285)(146,279)(147,282)(148,292)
(149,261)(150,271)(151,274)(152,268)(153,265)(154,275)(155,270)(156,264)
(157,273)(158,267)(159,262)(160,272)(161,269)(162,263)(163,266)(164,276);;
s4 := ( 5,277)( 6,278)( 7,280)( 8,279)( 9,282)( 10,281)( 11,283)( 12,284)
( 13,292)( 14,291)( 15,289)( 16,290)( 17,287)( 18,288)( 19,286)( 20,285)
( 21,261)( 22,262)( 23,264)( 24,263)( 25,266)( 26,265)( 27,267)( 28,268)
( 29,276)( 30,275)( 31,273)( 32,274)( 33,271)( 34,272)( 35,270)( 36,269)
( 37,245)( 38,246)( 39,248)( 40,247)( 41,250)( 42,249)( 43,251)( 44,252)
( 45,260)( 46,259)( 47,257)( 48,258)( 49,255)( 50,256)( 51,254)( 52,253)
( 53,309)( 54,310)( 55,312)( 56,311)( 57,314)( 58,313)( 59,315)( 60,316)
( 61,324)( 62,323)( 63,321)( 64,322)( 65,319)( 66,320)( 67,318)( 68,317)
( 69,293)( 70,294)( 71,296)( 72,295)( 73,298)( 74,297)( 75,299)( 76,300)
( 77,308)( 78,307)( 79,305)( 80,306)( 81,303)( 82,304)( 83,302)( 84,301)
( 85,197)( 86,198)( 87,200)( 88,199)( 89,202)( 90,201)( 91,203)( 92,204)
( 93,212)( 94,211)( 95,209)( 96,210)( 97,207)( 98,208)( 99,206)(100,205)
(101,181)(102,182)(103,184)(104,183)(105,186)(106,185)(107,187)(108,188)
(109,196)(110,195)(111,193)(112,194)(113,191)(114,192)(115,190)(116,189)
(117,165)(118,166)(119,168)(120,167)(121,170)(122,169)(123,171)(124,172)
(125,180)(126,179)(127,177)(128,178)(129,175)(130,176)(131,174)(132,173)
(133,229)(134,230)(135,232)(136,231)(137,234)(138,233)(139,235)(140,236)
(141,244)(142,243)(143,241)(144,242)(145,239)(146,240)(147,238)(148,237)
(149,213)(150,214)(151,216)(152,215)(153,218)(154,217)(155,219)(156,220)
(157,228)(158,227)(159,225)(160,226)(161,223)(162,224)(163,222)(164,221);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4,
s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(324)!(1,2);
s1 := Sym(324)!(3,4);
s2 := Sym(324)!( 5, 86)( 6, 85)( 7, 88)( 8, 87)( 9, 90)( 10, 89)( 11, 92)
( 12, 91)( 13, 94)( 14, 93)( 15, 96)( 16, 95)( 17, 98)( 18, 97)( 19,100)
( 20, 99)( 21,102)( 22,101)( 23,104)( 24,103)( 25,106)( 26,105)( 27,108)
( 28,107)( 29,110)( 30,109)( 31,112)( 32,111)( 33,114)( 34,113)( 35,116)
( 36,115)( 37,118)( 38,117)( 39,120)( 40,119)( 41,122)( 42,121)( 43,124)
( 44,123)( 45,126)( 46,125)( 47,128)( 48,127)( 49,130)( 50,129)( 51,132)
( 52,131)( 53,134)( 54,133)( 55,136)( 56,135)( 57,138)( 58,137)( 59,140)
( 60,139)( 61,142)( 62,141)( 63,144)( 64,143)( 65,146)( 66,145)( 67,148)
( 68,147)( 69,150)( 70,149)( 71,152)( 72,151)( 73,154)( 74,153)( 75,156)
( 76,155)( 77,158)( 78,157)( 79,160)( 80,159)( 81,162)( 82,161)( 83,164)
( 84,163)(165,246)(166,245)(167,248)(168,247)(169,250)(170,249)(171,252)
(172,251)(173,254)(174,253)(175,256)(176,255)(177,258)(178,257)(179,260)
(180,259)(181,262)(182,261)(183,264)(184,263)(185,266)(186,265)(187,268)
(188,267)(189,270)(190,269)(191,272)(192,271)(193,274)(194,273)(195,276)
(196,275)(197,278)(198,277)(199,280)(200,279)(201,282)(202,281)(203,284)
(204,283)(205,286)(206,285)(207,288)(208,287)(209,290)(210,289)(211,292)
(212,291)(213,294)(214,293)(215,296)(216,295)(217,298)(218,297)(219,300)
(220,299)(221,302)(222,301)(223,304)(224,303)(225,306)(226,305)(227,308)
(228,307)(229,310)(230,309)(231,312)(232,311)(233,314)(234,313)(235,316)
(236,315)(237,318)(238,317)(239,320)(240,319)(241,322)(242,321)(243,324)
(244,323);
s3 := Sym(324)!( 5,165)( 6,175)( 7,178)( 8,172)( 9,169)( 10,179)( 11,174)
( 12,168)( 13,177)( 14,171)( 15,166)( 16,176)( 17,173)( 18,167)( 19,170)
( 20,180)( 21,229)( 22,239)( 23,242)( 24,236)( 25,233)( 26,243)( 27,238)
( 28,232)( 29,241)( 30,235)( 31,230)( 32,240)( 33,237)( 34,231)( 35,234)
( 36,244)( 37,213)( 38,223)( 39,226)( 40,220)( 41,217)( 42,227)( 43,222)
( 44,216)( 45,225)( 46,219)( 47,214)( 48,224)( 49,221)( 50,215)( 51,218)
( 52,228)( 53,197)( 54,207)( 55,210)( 56,204)( 57,201)( 58,211)( 59,206)
( 60,200)( 61,209)( 62,203)( 63,198)( 64,208)( 65,205)( 66,199)( 67,202)
( 68,212)( 69,181)( 70,191)( 71,194)( 72,188)( 73,185)( 74,195)( 75,190)
( 76,184)( 77,193)( 78,187)( 79,182)( 80,192)( 81,189)( 82,183)( 83,186)
( 84,196)( 85,245)( 86,255)( 87,258)( 88,252)( 89,249)( 90,259)( 91,254)
( 92,248)( 93,257)( 94,251)( 95,246)( 96,256)( 97,253)( 98,247)( 99,250)
(100,260)(101,309)(102,319)(103,322)(104,316)(105,313)(106,323)(107,318)
(108,312)(109,321)(110,315)(111,310)(112,320)(113,317)(114,311)(115,314)
(116,324)(117,293)(118,303)(119,306)(120,300)(121,297)(122,307)(123,302)
(124,296)(125,305)(126,299)(127,294)(128,304)(129,301)(130,295)(131,298)
(132,308)(133,277)(134,287)(135,290)(136,284)(137,281)(138,291)(139,286)
(140,280)(141,289)(142,283)(143,278)(144,288)(145,285)(146,279)(147,282)
(148,292)(149,261)(150,271)(151,274)(152,268)(153,265)(154,275)(155,270)
(156,264)(157,273)(158,267)(159,262)(160,272)(161,269)(162,263)(163,266)
(164,276);
s4 := Sym(324)!( 5,277)( 6,278)( 7,280)( 8,279)( 9,282)( 10,281)( 11,283)
( 12,284)( 13,292)( 14,291)( 15,289)( 16,290)( 17,287)( 18,288)( 19,286)
( 20,285)( 21,261)( 22,262)( 23,264)( 24,263)( 25,266)( 26,265)( 27,267)
( 28,268)( 29,276)( 30,275)( 31,273)( 32,274)( 33,271)( 34,272)( 35,270)
( 36,269)( 37,245)( 38,246)( 39,248)( 40,247)( 41,250)( 42,249)( 43,251)
( 44,252)( 45,260)( 46,259)( 47,257)( 48,258)( 49,255)( 50,256)( 51,254)
( 52,253)( 53,309)( 54,310)( 55,312)( 56,311)( 57,314)( 58,313)( 59,315)
( 60,316)( 61,324)( 62,323)( 63,321)( 64,322)( 65,319)( 66,320)( 67,318)
( 68,317)( 69,293)( 70,294)( 71,296)( 72,295)( 73,298)( 74,297)( 75,299)
( 76,300)( 77,308)( 78,307)( 79,305)( 80,306)( 81,303)( 82,304)( 83,302)
( 84,301)( 85,197)( 86,198)( 87,200)( 88,199)( 89,202)( 90,201)( 91,203)
( 92,204)( 93,212)( 94,211)( 95,209)( 96,210)( 97,207)( 98,208)( 99,206)
(100,205)(101,181)(102,182)(103,184)(104,183)(105,186)(106,185)(107,187)
(108,188)(109,196)(110,195)(111,193)(112,194)(113,191)(114,192)(115,190)
(116,189)(117,165)(118,166)(119,168)(120,167)(121,170)(122,169)(123,171)
(124,172)(125,180)(126,179)(127,177)(128,178)(129,175)(130,176)(131,174)
(132,173)(133,229)(134,230)(135,232)(136,231)(137,234)(138,233)(139,235)
(140,236)(141,244)(142,243)(143,241)(144,242)(145,239)(146,240)(147,238)
(148,237)(149,213)(150,214)(151,216)(152,215)(153,218)(154,217)(155,219)
(156,220)(157,228)(158,227)(159,225)(160,226)(161,223)(162,224)(163,222)
(164,221);
poly := sub<Sym(324)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4,
s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3 >;
to this polytope