Polytope of Type {3,2,8,5}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,8,5}*1920a
if this polytope has a name.
Group : SmallGroup(1920,240046)
Rank : 5
Schlafli Type : {3,2,8,5}
Number of vertices, edges, etc : 3, 3, 32, 80, 20
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, 6)( 5, 7)( 8, 10)( 9, 11)( 12, 14)( 13, 15)( 16, 18)( 17, 19)
( 20, 22)( 21, 23)( 24, 26)( 25, 27)( 28, 30)( 29, 31)( 32, 34)( 33, 35)
( 36, 38)( 37, 39)( 40, 42)( 41, 43)( 44, 46)( 45, 47)( 48, 50)( 49, 51)
( 52, 54)( 53, 55)( 56, 58)( 57, 59)( 60, 62)( 61, 63)( 64, 66)( 65, 67)
( 68, 70)( 69, 71)( 72, 74)( 73, 75)( 76, 78)( 77, 79)( 80, 82)( 81, 83)
( 84, 86)( 85, 87)( 88, 90)( 89, 91)( 92, 94)( 93, 95)( 96, 98)( 97, 99)
(100,102)(101,103)(104,106)(105,107)(108,110)(109,111)(112,114)(113,115)
(116,118)(117,119)(120,122)(121,123)(124,126)(125,127)(128,130)(129,131)
(132,134)(133,135)(136,138)(137,139)(140,142)(141,143)(144,146)(145,147)
(148,150)(149,151)(152,154)(153,155)(156,158)(157,159)(160,162)(161,163)
(164,166)(165,167)(168,170)(169,171)(172,174)(173,175)(176,178)(177,179)
(180,182)(181,183)(184,186)(185,187)(188,190)(189,191)(192,194)(193,195)
(196,198)(197,199)(200,202)(201,203)(204,206)(205,207)(208,210)(209,211)
(212,214)(213,215)(216,218)(217,219)(220,222)(221,223)(224,226)(225,227)
(228,230)(229,231)(232,234)(233,235)(236,238)(237,239)(240,242)(241,243)
(244,246)(245,247)(248,250)(249,251)(252,254)(253,255)(256,258)(257,259)
(260,262)(261,263)(264,266)(265,267)(268,270)(269,271)(272,274)(273,275)
(276,278)(277,279)(280,282)(281,283)(284,286)(285,287)(288,290)(289,291)
(292,294)(293,295)(296,298)(297,299)(300,302)(301,303)(304,306)(305,307)
(308,310)(309,311)(312,314)(313,315)(316,318)(317,319)(320,322)(321,323);;
s3 := ( 4,164)( 5,165)( 6,184)( 7,185)( 8,190)( 9,191)( 10,178)( 11,179)
( 12,173)( 13,172)( 14,192)( 15,193)( 16,183)( 17,182)( 18,170)( 19,171)
( 20,188)( 21,189)( 22,177)( 23,176)( 24,166)( 25,167)( 26,187)( 27,186)
( 28,180)( 29,181)( 30,168)( 31,169)( 32,174)( 33,175)( 34,194)( 35,195)
( 36,292)( 37,293)( 38,312)( 39,313)( 40,318)( 41,319)( 42,306)( 43,307)
( 44,301)( 45,300)( 46,320)( 47,321)( 48,311)( 49,310)( 50,298)( 51,299)
( 52,316)( 53,317)( 54,305)( 55,304)( 56,294)( 57,295)( 58,315)( 59,314)
( 60,308)( 61,309)( 62,296)( 63,297)( 64,302)( 65,303)( 66,322)( 67,323)
( 68,260)( 69,261)( 70,280)( 71,281)( 72,286)( 73,287)( 74,274)( 75,275)
( 76,269)( 77,268)( 78,288)( 79,289)( 80,279)( 81,278)( 82,266)( 83,267)
( 84,284)( 85,285)( 86,273)( 87,272)( 88,262)( 89,263)( 90,283)( 91,282)
( 92,276)( 93,277)( 94,264)( 95,265)( 96,270)( 97,271)( 98,290)( 99,291)
(100,228)(101,229)(102,248)(103,249)(104,254)(105,255)(106,242)(107,243)
(108,237)(109,236)(110,256)(111,257)(112,247)(113,246)(114,234)(115,235)
(116,252)(117,253)(118,241)(119,240)(120,230)(121,231)(122,251)(123,250)
(124,244)(125,245)(126,232)(127,233)(128,238)(129,239)(130,258)(131,259)
(132,196)(133,197)(134,216)(135,217)(136,222)(137,223)(138,210)(139,211)
(140,205)(141,204)(142,224)(143,225)(144,215)(145,214)(146,202)(147,203)
(148,220)(149,221)(150,209)(151,208)(152,198)(153,199)(154,219)(155,218)
(156,212)(157,213)(158,200)(159,201)(160,206)(161,207)(162,226)(163,227);;
s4 := ( 4,228)( 5,229)( 6,230)( 7,231)( 8,235)( 9,234)( 10,233)( 11,232)
( 12,238)( 13,239)( 14,236)( 15,237)( 16,241)( 17,240)( 18,243)( 19,242)
( 20,259)( 21,258)( 22,257)( 23,256)( 24,253)( 25,252)( 26,255)( 27,254)
( 28,249)( 29,248)( 30,251)( 31,250)( 32,247)( 33,246)( 34,245)( 35,244)
( 36,196)( 37,197)( 38,198)( 39,199)( 40,203)( 41,202)( 42,201)( 43,200)
( 44,206)( 45,207)( 46,204)( 47,205)( 48,209)( 49,208)( 50,211)( 51,210)
( 52,227)( 53,226)( 54,225)( 55,224)( 56,221)( 57,220)( 58,223)( 59,222)
( 60,217)( 61,216)( 62,219)( 63,218)( 64,215)( 65,214)( 66,213)( 67,212)
( 68,164)( 69,165)( 70,166)( 71,167)( 72,171)( 73,170)( 74,169)( 75,168)
( 76,174)( 77,175)( 78,172)( 79,173)( 80,177)( 81,176)( 82,179)( 83,178)
( 84,195)( 85,194)( 86,193)( 87,192)( 88,189)( 89,188)( 90,191)( 91,190)
( 92,185)( 93,184)( 94,187)( 95,186)( 96,183)( 97,182)( 98,181)( 99,180)
(100,292)(101,293)(102,294)(103,295)(104,299)(105,298)(106,297)(107,296)
(108,302)(109,303)(110,300)(111,301)(112,305)(113,304)(114,307)(115,306)
(116,323)(117,322)(118,321)(119,320)(120,317)(121,316)(122,319)(123,318)
(124,313)(125,312)(126,315)(127,314)(128,311)(129,310)(130,309)(131,308)
(132,260)(133,261)(134,262)(135,263)(136,267)(137,266)(138,265)(139,264)
(140,270)(141,271)(142,268)(143,269)(144,273)(145,272)(146,275)(147,274)
(148,291)(149,290)(150,289)(151,288)(152,285)(153,284)(154,287)(155,286)
(156,281)(157,280)(158,283)(159,282)(160,279)(161,278)(162,277)(163,276);;
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, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s2*s3*s2*s3*s4*s3*s2*s3*s2*s3,
s4*s3*s2*s4*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s4*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(323)!(2,3);
s1 := Sym(323)!(1,2);
s2 := Sym(323)!( 4, 6)( 5, 7)( 8, 10)( 9, 11)( 12, 14)( 13, 15)( 16, 18)
( 17, 19)( 20, 22)( 21, 23)( 24, 26)( 25, 27)( 28, 30)( 29, 31)( 32, 34)
( 33, 35)( 36, 38)( 37, 39)( 40, 42)( 41, 43)( 44, 46)( 45, 47)( 48, 50)
( 49, 51)( 52, 54)( 53, 55)( 56, 58)( 57, 59)( 60, 62)( 61, 63)( 64, 66)
( 65, 67)( 68, 70)( 69, 71)( 72, 74)( 73, 75)( 76, 78)( 77, 79)( 80, 82)
( 81, 83)( 84, 86)( 85, 87)( 88, 90)( 89, 91)( 92, 94)( 93, 95)( 96, 98)
( 97, 99)(100,102)(101,103)(104,106)(105,107)(108,110)(109,111)(112,114)
(113,115)(116,118)(117,119)(120,122)(121,123)(124,126)(125,127)(128,130)
(129,131)(132,134)(133,135)(136,138)(137,139)(140,142)(141,143)(144,146)
(145,147)(148,150)(149,151)(152,154)(153,155)(156,158)(157,159)(160,162)
(161,163)(164,166)(165,167)(168,170)(169,171)(172,174)(173,175)(176,178)
(177,179)(180,182)(181,183)(184,186)(185,187)(188,190)(189,191)(192,194)
(193,195)(196,198)(197,199)(200,202)(201,203)(204,206)(205,207)(208,210)
(209,211)(212,214)(213,215)(216,218)(217,219)(220,222)(221,223)(224,226)
(225,227)(228,230)(229,231)(232,234)(233,235)(236,238)(237,239)(240,242)
(241,243)(244,246)(245,247)(248,250)(249,251)(252,254)(253,255)(256,258)
(257,259)(260,262)(261,263)(264,266)(265,267)(268,270)(269,271)(272,274)
(273,275)(276,278)(277,279)(280,282)(281,283)(284,286)(285,287)(288,290)
(289,291)(292,294)(293,295)(296,298)(297,299)(300,302)(301,303)(304,306)
(305,307)(308,310)(309,311)(312,314)(313,315)(316,318)(317,319)(320,322)
(321,323);
s3 := Sym(323)!( 4,164)( 5,165)( 6,184)( 7,185)( 8,190)( 9,191)( 10,178)
( 11,179)( 12,173)( 13,172)( 14,192)( 15,193)( 16,183)( 17,182)( 18,170)
( 19,171)( 20,188)( 21,189)( 22,177)( 23,176)( 24,166)( 25,167)( 26,187)
( 27,186)( 28,180)( 29,181)( 30,168)( 31,169)( 32,174)( 33,175)( 34,194)
( 35,195)( 36,292)( 37,293)( 38,312)( 39,313)( 40,318)( 41,319)( 42,306)
( 43,307)( 44,301)( 45,300)( 46,320)( 47,321)( 48,311)( 49,310)( 50,298)
( 51,299)( 52,316)( 53,317)( 54,305)( 55,304)( 56,294)( 57,295)( 58,315)
( 59,314)( 60,308)( 61,309)( 62,296)( 63,297)( 64,302)( 65,303)( 66,322)
( 67,323)( 68,260)( 69,261)( 70,280)( 71,281)( 72,286)( 73,287)( 74,274)
( 75,275)( 76,269)( 77,268)( 78,288)( 79,289)( 80,279)( 81,278)( 82,266)
( 83,267)( 84,284)( 85,285)( 86,273)( 87,272)( 88,262)( 89,263)( 90,283)
( 91,282)( 92,276)( 93,277)( 94,264)( 95,265)( 96,270)( 97,271)( 98,290)
( 99,291)(100,228)(101,229)(102,248)(103,249)(104,254)(105,255)(106,242)
(107,243)(108,237)(109,236)(110,256)(111,257)(112,247)(113,246)(114,234)
(115,235)(116,252)(117,253)(118,241)(119,240)(120,230)(121,231)(122,251)
(123,250)(124,244)(125,245)(126,232)(127,233)(128,238)(129,239)(130,258)
(131,259)(132,196)(133,197)(134,216)(135,217)(136,222)(137,223)(138,210)
(139,211)(140,205)(141,204)(142,224)(143,225)(144,215)(145,214)(146,202)
(147,203)(148,220)(149,221)(150,209)(151,208)(152,198)(153,199)(154,219)
(155,218)(156,212)(157,213)(158,200)(159,201)(160,206)(161,207)(162,226)
(163,227);
s4 := Sym(323)!( 4,228)( 5,229)( 6,230)( 7,231)( 8,235)( 9,234)( 10,233)
( 11,232)( 12,238)( 13,239)( 14,236)( 15,237)( 16,241)( 17,240)( 18,243)
( 19,242)( 20,259)( 21,258)( 22,257)( 23,256)( 24,253)( 25,252)( 26,255)
( 27,254)( 28,249)( 29,248)( 30,251)( 31,250)( 32,247)( 33,246)( 34,245)
( 35,244)( 36,196)( 37,197)( 38,198)( 39,199)( 40,203)( 41,202)( 42,201)
( 43,200)( 44,206)( 45,207)( 46,204)( 47,205)( 48,209)( 49,208)( 50,211)
( 51,210)( 52,227)( 53,226)( 54,225)( 55,224)( 56,221)( 57,220)( 58,223)
( 59,222)( 60,217)( 61,216)( 62,219)( 63,218)( 64,215)( 65,214)( 66,213)
( 67,212)( 68,164)( 69,165)( 70,166)( 71,167)( 72,171)( 73,170)( 74,169)
( 75,168)( 76,174)( 77,175)( 78,172)( 79,173)( 80,177)( 81,176)( 82,179)
( 83,178)( 84,195)( 85,194)( 86,193)( 87,192)( 88,189)( 89,188)( 90,191)
( 91,190)( 92,185)( 93,184)( 94,187)( 95,186)( 96,183)( 97,182)( 98,181)
( 99,180)(100,292)(101,293)(102,294)(103,295)(104,299)(105,298)(106,297)
(107,296)(108,302)(109,303)(110,300)(111,301)(112,305)(113,304)(114,307)
(115,306)(116,323)(117,322)(118,321)(119,320)(120,317)(121,316)(122,319)
(123,318)(124,313)(125,312)(126,315)(127,314)(128,311)(129,310)(130,309)
(131,308)(132,260)(133,261)(134,262)(135,263)(136,267)(137,266)(138,265)
(139,264)(140,270)(141,271)(142,268)(143,269)(144,273)(145,272)(146,275)
(147,274)(148,291)(149,290)(150,289)(151,288)(152,285)(153,284)(154,287)
(155,286)(156,281)(157,280)(158,283)(159,282)(160,279)(161,278)(162,277)
(163,276);
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,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s2*s3*s2*s3*s4*s3*s2*s3*s2*s3,
s4*s3*s2*s4*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s4*s3*s2 >;
to this polytope