Polytope of Type {3,2,4,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,4,10}*1920a
if this polytope has a name.
Group : SmallGroup(1920,240399)
Rank : 5
Schlafli Type : {3,2,4,10}
Number of vertices, edges, etc : 3, 3, 16, 80, 40
Order of s0s1s2s3s4 : 30
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 : {3,2,4,5}*960
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 4, 5)( 6, 7)( 8, 9)( 10, 11)( 12, 13)( 14, 15)( 16, 17)( 18, 19)
( 20, 21)( 22, 23)( 24, 25)( 26, 27)( 28, 29)( 30, 31)( 32, 33)( 34, 35)
( 36, 37)( 38, 39)( 40, 41)( 42, 43)( 44, 45)( 46, 47)( 48, 49)( 50, 51)
( 52, 53)( 54, 55)( 56, 57)( 58, 59)( 60, 61)( 62, 63)( 64, 65)( 66, 67)
( 68, 69)( 70, 71)( 72, 73)( 74, 75)( 76, 77)( 78, 79)( 80, 81)( 82, 83)
( 84, 85)( 86, 87)( 88, 89)( 90, 91)( 92, 93)( 94, 95)( 96, 97)( 98, 99)
(100,101)(102,103)(104,105)(106,107)(108,109)(110,111)(112,113)(114,115)
(116,117)(118,119)(120,121)(122,123)(124,125)(126,127)(128,129)(130,131)
(132,133)(134,135)(136,137)(138,139)(140,141)(142,143)(144,145)(146,147)
(148,149)(150,151)(152,153)(154,155)(156,157)(158,159)(160,161)(162,163)
(164,165)(166,167)(168,169)(170,171)(172,173)(174,175)(176,177)(178,179)
(180,181)(182,183)(184,185)(186,187)(188,189)(190,191)(192,193)(194,195)
(196,197)(198,199)(200,201)(202,203)(204,205)(206,207)(208,209)(210,211)
(212,213)(214,215)(216,217)(218,219)(220,221)(222,223)(224,225)(226,227)
(228,229)(230,231)(232,233)(234,235)(236,237)(238,239)(240,241)(242,243)
(244,245)(246,247)(248,249)(250,251)(252,253)(254,255)(256,257)(258,259)
(260,261)(262,263)(264,265)(266,267)(268,269)(270,271)(272,273)(274,275)
(276,277)(278,279)(280,281)(282,283)(284,285)(286,287)(288,289)(290,291)
(292,293)(294,295)(296,297)(298,299)(300,301)(302,303)(304,305)(306,307)
(308,309)(310,311)(312,313)(314,315)(316,317)(318,319)(320,321)(322,323);;
s3 := ( 4,164)( 5,174)( 6,177)( 7,171)( 8,168)( 9,178)( 10,173)( 11,167)
( 12,176)( 13,170)( 14,165)( 15,175)( 16,172)( 17,166)( 18,169)( 19,179)
( 20,228)( 21,238)( 22,241)( 23,235)( 24,232)( 25,242)( 26,237)( 27,231)
( 28,240)( 29,234)( 30,229)( 31,239)( 32,236)( 33,230)( 34,233)( 35,243)
( 36,212)( 37,222)( 38,225)( 39,219)( 40,216)( 41,226)( 42,221)( 43,215)
( 44,224)( 45,218)( 46,213)( 47,223)( 48,220)( 49,214)( 50,217)( 51,227)
( 52,196)( 53,206)( 54,209)( 55,203)( 56,200)( 57,210)( 58,205)( 59,199)
( 60,208)( 61,202)( 62,197)( 63,207)( 64,204)( 65,198)( 66,201)( 67,211)
( 68,180)( 69,190)( 70,193)( 71,187)( 72,184)( 73,194)( 74,189)( 75,183)
( 76,192)( 77,186)( 78,181)( 79,191)( 80,188)( 81,182)( 82,185)( 83,195)
( 84,244)( 85,254)( 86,257)( 87,251)( 88,248)( 89,258)( 90,253)( 91,247)
( 92,256)( 93,250)( 94,245)( 95,255)( 96,252)( 97,246)( 98,249)( 99,259)
(100,308)(101,318)(102,321)(103,315)(104,312)(105,322)(106,317)(107,311)
(108,320)(109,314)(110,309)(111,319)(112,316)(113,310)(114,313)(115,323)
(116,292)(117,302)(118,305)(119,299)(120,296)(121,306)(122,301)(123,295)
(124,304)(125,298)(126,293)(127,303)(128,300)(129,294)(130,297)(131,307)
(132,276)(133,286)(134,289)(135,283)(136,280)(137,290)(138,285)(139,279)
(140,288)(141,282)(142,277)(143,287)(144,284)(145,278)(146,281)(147,291)
(148,260)(149,270)(150,273)(151,267)(152,264)(153,274)(154,269)(155,263)
(156,272)(157,266)(158,261)(159,271)(160,268)(161,262)(162,265)(163,275);;
s4 := ( 4,276)( 5,277)( 6,279)( 7,278)( 8,281)( 9,280)( 10,282)( 11,283)
( 12,291)( 13,290)( 14,288)( 15,289)( 16,286)( 17,287)( 18,285)( 19,284)
( 20,260)( 21,261)( 22,263)( 23,262)( 24,265)( 25,264)( 26,266)( 27,267)
( 28,275)( 29,274)( 30,272)( 31,273)( 32,270)( 33,271)( 34,269)( 35,268)
( 36,244)( 37,245)( 38,247)( 39,246)( 40,249)( 41,248)( 42,250)( 43,251)
( 44,259)( 45,258)( 46,256)( 47,257)( 48,254)( 49,255)( 50,253)( 51,252)
( 52,308)( 53,309)( 54,311)( 55,310)( 56,313)( 57,312)( 58,314)( 59,315)
( 60,323)( 61,322)( 62,320)( 63,321)( 64,318)( 65,319)( 66,317)( 67,316)
( 68,292)( 69,293)( 70,295)( 71,294)( 72,297)( 73,296)( 74,298)( 75,299)
( 76,307)( 77,306)( 78,304)( 79,305)( 80,302)( 81,303)( 82,301)( 83,300)
( 84,196)( 85,197)( 86,199)( 87,198)( 88,201)( 89,200)( 90,202)( 91,203)
( 92,211)( 93,210)( 94,208)( 95,209)( 96,206)( 97,207)( 98,205)( 99,204)
(100,180)(101,181)(102,183)(103,182)(104,185)(105,184)(106,186)(107,187)
(108,195)(109,194)(110,192)(111,193)(112,190)(113,191)(114,189)(115,188)
(116,164)(117,165)(118,167)(119,166)(120,169)(121,168)(122,170)(123,171)
(124,179)(125,178)(126,176)(127,177)(128,174)(129,175)(130,173)(131,172)
(132,228)(133,229)(134,231)(135,230)(136,233)(137,232)(138,234)(139,235)
(140,243)(141,242)(142,240)(143,241)(144,238)(145,239)(146,237)(147,236)
(148,212)(149,213)(150,215)(151,214)(152,217)(153,216)(154,218)(155,219)
(156,227)(157,226)(158,224)(159,225)(160,222)(161,223)(162,221)(163,220);;
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*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,
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3,
s3*s2*s3*s4*s2*s3*s4*s2*s3*s4*s3*s2*s3*s4*s2*s3*s4*s3*s4,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(323)!(2,3);
s1 := Sym(323)!(1,2);
s2 := Sym(323)!( 4, 5)( 6, 7)( 8, 9)( 10, 11)( 12, 13)( 14, 15)( 16, 17)
( 18, 19)( 20, 21)( 22, 23)( 24, 25)( 26, 27)( 28, 29)( 30, 31)( 32, 33)
( 34, 35)( 36, 37)( 38, 39)( 40, 41)( 42, 43)( 44, 45)( 46, 47)( 48, 49)
( 50, 51)( 52, 53)( 54, 55)( 56, 57)( 58, 59)( 60, 61)( 62, 63)( 64, 65)
( 66, 67)( 68, 69)( 70, 71)( 72, 73)( 74, 75)( 76, 77)( 78, 79)( 80, 81)
( 82, 83)( 84, 85)( 86, 87)( 88, 89)( 90, 91)( 92, 93)( 94, 95)( 96, 97)
( 98, 99)(100,101)(102,103)(104,105)(106,107)(108,109)(110,111)(112,113)
(114,115)(116,117)(118,119)(120,121)(122,123)(124,125)(126,127)(128,129)
(130,131)(132,133)(134,135)(136,137)(138,139)(140,141)(142,143)(144,145)
(146,147)(148,149)(150,151)(152,153)(154,155)(156,157)(158,159)(160,161)
(162,163)(164,165)(166,167)(168,169)(170,171)(172,173)(174,175)(176,177)
(178,179)(180,181)(182,183)(184,185)(186,187)(188,189)(190,191)(192,193)
(194,195)(196,197)(198,199)(200,201)(202,203)(204,205)(206,207)(208,209)
(210,211)(212,213)(214,215)(216,217)(218,219)(220,221)(222,223)(224,225)
(226,227)(228,229)(230,231)(232,233)(234,235)(236,237)(238,239)(240,241)
(242,243)(244,245)(246,247)(248,249)(250,251)(252,253)(254,255)(256,257)
(258,259)(260,261)(262,263)(264,265)(266,267)(268,269)(270,271)(272,273)
(274,275)(276,277)(278,279)(280,281)(282,283)(284,285)(286,287)(288,289)
(290,291)(292,293)(294,295)(296,297)(298,299)(300,301)(302,303)(304,305)
(306,307)(308,309)(310,311)(312,313)(314,315)(316,317)(318,319)(320,321)
(322,323);
s3 := Sym(323)!( 4,164)( 5,174)( 6,177)( 7,171)( 8,168)( 9,178)( 10,173)
( 11,167)( 12,176)( 13,170)( 14,165)( 15,175)( 16,172)( 17,166)( 18,169)
( 19,179)( 20,228)( 21,238)( 22,241)( 23,235)( 24,232)( 25,242)( 26,237)
( 27,231)( 28,240)( 29,234)( 30,229)( 31,239)( 32,236)( 33,230)( 34,233)
( 35,243)( 36,212)( 37,222)( 38,225)( 39,219)( 40,216)( 41,226)( 42,221)
( 43,215)( 44,224)( 45,218)( 46,213)( 47,223)( 48,220)( 49,214)( 50,217)
( 51,227)( 52,196)( 53,206)( 54,209)( 55,203)( 56,200)( 57,210)( 58,205)
( 59,199)( 60,208)( 61,202)( 62,197)( 63,207)( 64,204)( 65,198)( 66,201)
( 67,211)( 68,180)( 69,190)( 70,193)( 71,187)( 72,184)( 73,194)( 74,189)
( 75,183)( 76,192)( 77,186)( 78,181)( 79,191)( 80,188)( 81,182)( 82,185)
( 83,195)( 84,244)( 85,254)( 86,257)( 87,251)( 88,248)( 89,258)( 90,253)
( 91,247)( 92,256)( 93,250)( 94,245)( 95,255)( 96,252)( 97,246)( 98,249)
( 99,259)(100,308)(101,318)(102,321)(103,315)(104,312)(105,322)(106,317)
(107,311)(108,320)(109,314)(110,309)(111,319)(112,316)(113,310)(114,313)
(115,323)(116,292)(117,302)(118,305)(119,299)(120,296)(121,306)(122,301)
(123,295)(124,304)(125,298)(126,293)(127,303)(128,300)(129,294)(130,297)
(131,307)(132,276)(133,286)(134,289)(135,283)(136,280)(137,290)(138,285)
(139,279)(140,288)(141,282)(142,277)(143,287)(144,284)(145,278)(146,281)
(147,291)(148,260)(149,270)(150,273)(151,267)(152,264)(153,274)(154,269)
(155,263)(156,272)(157,266)(158,261)(159,271)(160,268)(161,262)(162,265)
(163,275);
s4 := Sym(323)!( 4,276)( 5,277)( 6,279)( 7,278)( 8,281)( 9,280)( 10,282)
( 11,283)( 12,291)( 13,290)( 14,288)( 15,289)( 16,286)( 17,287)( 18,285)
( 19,284)( 20,260)( 21,261)( 22,263)( 23,262)( 24,265)( 25,264)( 26,266)
( 27,267)( 28,275)( 29,274)( 30,272)( 31,273)( 32,270)( 33,271)( 34,269)
( 35,268)( 36,244)( 37,245)( 38,247)( 39,246)( 40,249)( 41,248)( 42,250)
( 43,251)( 44,259)( 45,258)( 46,256)( 47,257)( 48,254)( 49,255)( 50,253)
( 51,252)( 52,308)( 53,309)( 54,311)( 55,310)( 56,313)( 57,312)( 58,314)
( 59,315)( 60,323)( 61,322)( 62,320)( 63,321)( 64,318)( 65,319)( 66,317)
( 67,316)( 68,292)( 69,293)( 70,295)( 71,294)( 72,297)( 73,296)( 74,298)
( 75,299)( 76,307)( 77,306)( 78,304)( 79,305)( 80,302)( 81,303)( 82,301)
( 83,300)( 84,196)( 85,197)( 86,199)( 87,198)( 88,201)( 89,200)( 90,202)
( 91,203)( 92,211)( 93,210)( 94,208)( 95,209)( 96,206)( 97,207)( 98,205)
( 99,204)(100,180)(101,181)(102,183)(103,182)(104,185)(105,184)(106,186)
(107,187)(108,195)(109,194)(110,192)(111,193)(112,190)(113,191)(114,189)
(115,188)(116,164)(117,165)(118,167)(119,166)(120,169)(121,168)(122,170)
(123,171)(124,179)(125,178)(126,176)(127,177)(128,174)(129,175)(130,173)
(131,172)(132,228)(133,229)(134,231)(135,230)(136,233)(137,232)(138,234)
(139,235)(140,243)(141,242)(142,240)(143,241)(144,238)(145,239)(146,237)
(147,236)(148,212)(149,213)(150,215)(151,214)(152,217)(153,216)(154,218)
(155,219)(156,227)(157,226)(158,224)(159,225)(160,222)(161,223)(162,221)
(163,220);
poly := sub<Sym(323)|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*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, s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3,
s3*s2*s3*s4*s2*s3*s4*s2*s3*s4*s3*s2*s3*s4*s2*s3*s4*s3*s4,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope