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