Polytope of Type {3,2,4,5}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,4,5}*1920
if this polytope has a name.
Group : SmallGroup(1920,240399)
Rank : 5
Schlafli Type : {3,2,4,5}
Number of vertices, edges, etc : 3, 3, 32, 80, 40
Order of s0s1s2s3s4 : 30
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
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
16-fold quotients : {3,2,2,5}*120
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 4, 85)( 5, 84)( 6, 87)( 7, 86)( 8, 89)( 9, 88)( 10, 91)( 11, 90)
( 12, 93)( 13, 92)( 14, 95)( 15, 94)( 16, 97)( 17, 96)( 18, 99)( 19, 98)
( 20,101)( 21,100)( 22,103)( 23,102)( 24,105)( 25,104)( 26,107)( 27,106)
( 28,109)( 29,108)( 30,111)( 31,110)( 32,113)( 33,112)( 34,115)( 35,114)
( 36,117)( 37,116)( 38,119)( 39,118)( 40,121)( 41,120)( 42,123)( 43,122)
( 44,125)( 45,124)( 46,127)( 47,126)( 48,129)( 49,128)( 50,131)( 51,130)
( 52,133)( 53,132)( 54,135)( 55,134)( 56,137)( 57,136)( 58,139)( 59,138)
( 60,141)( 61,140)( 62,143)( 63,142)( 64,145)( 65,144)( 66,147)( 67,146)
( 68,149)( 69,148)( 70,151)( 71,150)( 72,153)( 73,152)( 74,155)( 75,154)
( 76,157)( 77,156)( 78,159)( 79,158)( 80,161)( 81,160)( 82,163)( 83,162)
(164,245)(165,244)(166,247)(167,246)(168,249)(169,248)(170,251)(171,250)
(172,253)(173,252)(174,255)(175,254)(176,257)(177,256)(178,259)(179,258)
(180,261)(181,260)(182,263)(183,262)(184,265)(185,264)(186,267)(187,266)
(188,269)(189,268)(190,271)(191,270)(192,273)(193,272)(194,275)(195,274)
(196,277)(197,276)(198,279)(199,278)(200,281)(201,280)(202,283)(203,282)
(204,285)(205,284)(206,287)(207,286)(208,289)(209,288)(210,291)(211,290)
(212,293)(213,292)(214,295)(215,294)(216,297)(217,296)(218,299)(219,298)
(220,301)(221,300)(222,303)(223,302)(224,305)(225,304)(226,307)(227,306)
(228,309)(229,308)(230,311)(231,310)(232,313)(233,312)(234,315)(235,314)
(236,317)(237,316)(238,319)(239,318)(240,321)(241,320)(242,323)(243,322);;
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 := ( 4,196)( 5,197)( 6,199)( 7,198)( 8,201)( 9,200)( 10,202)( 11,203)
( 12,211)( 13,210)( 14,208)( 15,209)( 16,206)( 17,207)( 18,205)( 19,204)
( 20,180)( 21,181)( 22,183)( 23,182)( 24,185)( 25,184)( 26,186)( 27,187)
( 28,195)( 29,194)( 30,192)( 31,193)( 32,190)( 33,191)( 34,189)( 35,188)
( 36,164)( 37,165)( 38,167)( 39,166)( 40,169)( 41,168)( 42,170)( 43,171)
( 44,179)( 45,178)( 46,176)( 47,177)( 48,174)( 49,175)( 50,173)( 51,172)
( 52,228)( 53,229)( 54,231)( 55,230)( 56,233)( 57,232)( 58,234)( 59,235)
( 60,243)( 61,242)( 62,240)( 63,241)( 64,238)( 65,239)( 66,237)( 67,236)
( 68,212)( 69,213)( 70,215)( 71,214)( 72,217)( 73,216)( 74,218)( 75,219)
( 76,227)( 77,226)( 78,224)( 79,225)( 80,222)( 81,223)( 82,221)( 83,220)
( 84,276)( 85,277)( 86,279)( 87,278)( 88,281)( 89,280)( 90,282)( 91,283)
( 92,291)( 93,290)( 94,288)( 95,289)( 96,286)( 97,287)( 98,285)( 99,284)
(100,260)(101,261)(102,263)(103,262)(104,265)(105,264)(106,266)(107,267)
(108,275)(109,274)(110,272)(111,273)(112,270)(113,271)(114,269)(115,268)
(116,244)(117,245)(118,247)(119,246)(120,249)(121,248)(122,250)(123,251)
(124,259)(125,258)(126,256)(127,257)(128,254)(129,255)(130,253)(131,252)
(132,308)(133,309)(134,311)(135,310)(136,313)(137,312)(138,314)(139,315)
(140,323)(141,322)(142,320)(143,321)(144,318)(145,319)(146,317)(147,316)
(148,292)(149,293)(150,295)(151,294)(152,297)(153,296)(154,298)(155,299)
(156,307)(157,306)(158,304)(159,305)(160,302)(161,303)(162,301)(163,300);;
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,
s3*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(323)!(2,3);
s1 := Sym(323)!(1,2);
s2 := Sym(323)!( 4, 85)( 5, 84)( 6, 87)( 7, 86)( 8, 89)( 9, 88)( 10, 91)
( 11, 90)( 12, 93)( 13, 92)( 14, 95)( 15, 94)( 16, 97)( 17, 96)( 18, 99)
( 19, 98)( 20,101)( 21,100)( 22,103)( 23,102)( 24,105)( 25,104)( 26,107)
( 27,106)( 28,109)( 29,108)( 30,111)( 31,110)( 32,113)( 33,112)( 34,115)
( 35,114)( 36,117)( 37,116)( 38,119)( 39,118)( 40,121)( 41,120)( 42,123)
( 43,122)( 44,125)( 45,124)( 46,127)( 47,126)( 48,129)( 49,128)( 50,131)
( 51,130)( 52,133)( 53,132)( 54,135)( 55,134)( 56,137)( 57,136)( 58,139)
( 59,138)( 60,141)( 61,140)( 62,143)( 63,142)( 64,145)( 65,144)( 66,147)
( 67,146)( 68,149)( 69,148)( 70,151)( 71,150)( 72,153)( 73,152)( 74,155)
( 75,154)( 76,157)( 77,156)( 78,159)( 79,158)( 80,161)( 81,160)( 82,163)
( 83,162)(164,245)(165,244)(166,247)(167,246)(168,249)(169,248)(170,251)
(171,250)(172,253)(173,252)(174,255)(175,254)(176,257)(177,256)(178,259)
(179,258)(180,261)(181,260)(182,263)(183,262)(184,265)(185,264)(186,267)
(187,266)(188,269)(189,268)(190,271)(191,270)(192,273)(193,272)(194,275)
(195,274)(196,277)(197,276)(198,279)(199,278)(200,281)(201,280)(202,283)
(203,282)(204,285)(205,284)(206,287)(207,286)(208,289)(209,288)(210,291)
(211,290)(212,293)(213,292)(214,295)(215,294)(216,297)(217,296)(218,299)
(219,298)(220,301)(221,300)(222,303)(223,302)(224,305)(225,304)(226,307)
(227,306)(228,309)(229,308)(230,311)(231,310)(232,313)(233,312)(234,315)
(235,314)(236,317)(237,316)(238,319)(239,318)(240,321)(241,320)(242,323)
(243,322);
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)!( 4,196)( 5,197)( 6,199)( 7,198)( 8,201)( 9,200)( 10,202)
( 11,203)( 12,211)( 13,210)( 14,208)( 15,209)( 16,206)( 17,207)( 18,205)
( 19,204)( 20,180)( 21,181)( 22,183)( 23,182)( 24,185)( 25,184)( 26,186)
( 27,187)( 28,195)( 29,194)( 30,192)( 31,193)( 32,190)( 33,191)( 34,189)
( 35,188)( 36,164)( 37,165)( 38,167)( 39,166)( 40,169)( 41,168)( 42,170)
( 43,171)( 44,179)( 45,178)( 46,176)( 47,177)( 48,174)( 49,175)( 50,173)
( 51,172)( 52,228)( 53,229)( 54,231)( 55,230)( 56,233)( 57,232)( 58,234)
( 59,235)( 60,243)( 61,242)( 62,240)( 63,241)( 64,238)( 65,239)( 66,237)
( 67,236)( 68,212)( 69,213)( 70,215)( 71,214)( 72,217)( 73,216)( 74,218)
( 75,219)( 76,227)( 77,226)( 78,224)( 79,225)( 80,222)( 81,223)( 82,221)
( 83,220)( 84,276)( 85,277)( 86,279)( 87,278)( 88,281)( 89,280)( 90,282)
( 91,283)( 92,291)( 93,290)( 94,288)( 95,289)( 96,286)( 97,287)( 98,285)
( 99,284)(100,260)(101,261)(102,263)(103,262)(104,265)(105,264)(106,266)
(107,267)(108,275)(109,274)(110,272)(111,273)(112,270)(113,271)(114,269)
(115,268)(116,244)(117,245)(118,247)(119,246)(120,249)(121,248)(122,250)
(123,251)(124,259)(125,258)(126,256)(127,257)(128,254)(129,255)(130,253)
(131,252)(132,308)(133,309)(134,311)(135,310)(136,313)(137,312)(138,314)
(139,315)(140,323)(141,322)(142,320)(143,321)(144,318)(145,319)(146,317)
(147,316)(148,292)(149,293)(150,295)(151,294)(152,297)(153,296)(154,298)
(155,299)(156,307)(157,306)(158,304)(159,305)(160,302)(161,303)(162,301)
(163,300);
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, s3*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 >;
to this polytope