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}*1280a
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, 9)( 6, 10)( 7, 11)( 8, 12)( 13, 17)( 14, 18)( 15, 19)( 16, 20)
( 21, 25)( 22, 26)( 23, 27)( 24, 28)( 29, 33)( 30, 34)( 31, 35)( 32, 36)
( 37, 41)( 38, 42)( 39, 43)( 40, 44)( 45, 49)( 46, 50)( 47, 51)( 48, 52)
( 53, 57)( 54, 58)( 55, 59)( 56, 60)( 61, 65)( 62, 66)( 63, 67)( 64, 68)
( 69, 73)( 70, 74)( 71, 75)( 72, 76)( 77, 81)( 78, 82)( 79, 83)( 80, 84)
( 85, 89)( 86, 90)( 87, 91)( 88, 92)( 93, 97)( 94, 98)( 95, 99)( 96,100)
(101,105)(102,106)(103,107)(104,108)(109,113)(110,114)(111,115)(112,116)
(117,121)(118,122)(119,123)(120,124)(125,129)(126,130)(127,131)(128,132)
(133,137)(134,138)(135,139)(136,140)(141,145)(142,146)(143,147)(144,148)
(149,153)(150,154)(151,155)(152,156)(157,161)(158,162)(159,163)(160,164)
(165,169)(166,170)(167,171)(168,172)(173,177)(174,178)(175,179)(176,180)
(181,185)(182,186)(183,187)(184,188)(189,193)(190,194)(191,195)(192,196)
(197,201)(198,202)(199,203)(200,204)(205,209)(206,210)(207,211)(208,212)
(213,217)(214,218)(215,219)(216,220)(221,225)(222,226)(223,227)(224,228)
(229,233)(230,234)(231,235)(232,236)(237,241)(238,242)(239,243)(240,244)
(245,249)(246,250)(247,251)(248,252)(253,257)(254,258)(255,259)(256,260)
(261,265)(262,266)(263,267)(264,268)(269,273)(270,274)(271,275)(272,276)
(277,281)(278,282)(279,283)(280,284)(285,289)(286,290)(287,291)(288,292)
(293,297)(294,298)(295,299)(296,300)(301,305)(302,306)(303,307)(304,308)
(309,313)(310,314)(311,315)(312,316)(317,321)(318,322)(319,323)(320,324);;
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*s3*s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3,
s2*s3*s2*s3*s2*s4*s3*s4*s3*s2*s3*s4*s2*s3*s4*s2*s3*s4*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*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, 9)( 6, 10)( 7, 11)( 8, 12)( 13, 17)( 14, 18)( 15, 19)
( 16, 20)( 21, 25)( 22, 26)( 23, 27)( 24, 28)( 29, 33)( 30, 34)( 31, 35)
( 32, 36)( 37, 41)( 38, 42)( 39, 43)( 40, 44)( 45, 49)( 46, 50)( 47, 51)
( 48, 52)( 53, 57)( 54, 58)( 55, 59)( 56, 60)( 61, 65)( 62, 66)( 63, 67)
( 64, 68)( 69, 73)( 70, 74)( 71, 75)( 72, 76)( 77, 81)( 78, 82)( 79, 83)
( 80, 84)( 85, 89)( 86, 90)( 87, 91)( 88, 92)( 93, 97)( 94, 98)( 95, 99)
( 96,100)(101,105)(102,106)(103,107)(104,108)(109,113)(110,114)(111,115)
(112,116)(117,121)(118,122)(119,123)(120,124)(125,129)(126,130)(127,131)
(128,132)(133,137)(134,138)(135,139)(136,140)(141,145)(142,146)(143,147)
(144,148)(149,153)(150,154)(151,155)(152,156)(157,161)(158,162)(159,163)
(160,164)(165,169)(166,170)(167,171)(168,172)(173,177)(174,178)(175,179)
(176,180)(181,185)(182,186)(183,187)(184,188)(189,193)(190,194)(191,195)
(192,196)(197,201)(198,202)(199,203)(200,204)(205,209)(206,210)(207,211)
(208,212)(213,217)(214,218)(215,219)(216,220)(221,225)(222,226)(223,227)
(224,228)(229,233)(230,234)(231,235)(232,236)(237,241)(238,242)(239,243)
(240,244)(245,249)(246,250)(247,251)(248,252)(253,257)(254,258)(255,259)
(256,260)(261,265)(262,266)(263,267)(264,268)(269,273)(270,274)(271,275)
(272,276)(277,281)(278,282)(279,283)(280,284)(285,289)(286,290)(287,291)
(288,292)(293,297)(294,298)(295,299)(296,300)(301,305)(302,306)(303,307)
(304,308)(309,313)(310,314)(311,315)(312,316)(317,321)(318,322)(319,323)
(320,324);
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*s3*s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3,
s2*s3*s2*s3*s2*s4*s3*s4*s3*s2*s3*s4*s2*s3*s4*s2*s3*s4*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope