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