Polytope of Type {2,2,4,5}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,5}*1280
if this polytope has a name.
Group : SmallGroup(1280,1116461)
Rank : 5
Schlafli Type : {2,2,4,5}
Number of vertices, edges, etc : 2, 2, 32, 80, 40
Order of s0s1s2s3s4 : 10
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 : {2,2,4,5}*640
16-fold quotients : {2,2,2,5}*80
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 5, 86)( 6, 85)( 7, 88)( 8, 87)( 9, 90)( 10, 89)( 11, 92)( 12, 91)
( 13, 94)( 14, 93)( 15, 96)( 16, 95)( 17, 98)( 18, 97)( 19,100)( 20, 99)
( 21,102)( 22,101)( 23,104)( 24,103)( 25,106)( 26,105)( 27,108)( 28,107)
( 29,110)( 30,109)( 31,112)( 32,111)( 33,114)( 34,113)( 35,116)( 36,115)
( 37,118)( 38,117)( 39,120)( 40,119)( 41,122)( 42,121)( 43,124)( 44,123)
( 45,126)( 46,125)( 47,128)( 48,127)( 49,130)( 50,129)( 51,132)( 52,131)
( 53,134)( 54,133)( 55,136)( 56,135)( 57,138)( 58,137)( 59,140)( 60,139)
( 61,142)( 62,141)( 63,144)( 64,143)( 65,146)( 66,145)( 67,148)( 68,147)
( 69,150)( 70,149)( 71,152)( 72,151)( 73,154)( 74,153)( 75,156)( 76,155)
( 77,158)( 78,157)( 79,160)( 80,159)( 81,162)( 82,161)( 83,164)( 84,163)
(165,246)(166,245)(167,248)(168,247)(169,250)(170,249)(171,252)(172,251)
(173,254)(174,253)(175,256)(176,255)(177,258)(178,257)(179,260)(180,259)
(181,262)(182,261)(183,264)(184,263)(185,266)(186,265)(187,268)(188,267)
(189,270)(190,269)(191,272)(192,271)(193,274)(194,273)(195,276)(196,275)
(197,278)(198,277)(199,280)(200,279)(201,282)(202,281)(203,284)(204,283)
(205,286)(206,285)(207,288)(208,287)(209,290)(210,289)(211,292)(212,291)
(213,294)(214,293)(215,296)(216,295)(217,298)(218,297)(219,300)(220,299)
(221,302)(222,301)(223,304)(224,303)(225,306)(226,305)(227,308)(228,307)
(229,310)(230,309)(231,312)(232,311)(233,314)(234,313)(235,316)(236,315)
(237,318)(238,317)(239,320)(240,319)(241,322)(242,321)(243,324)(244,323);;
s3 := ( 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);;
s4 := ( 5,197)( 6,198)( 7,200)( 8,199)( 9,202)( 10,201)( 11,203)( 12,204)
( 13,212)( 14,211)( 15,209)( 16,210)( 17,207)( 18,208)( 19,206)( 20,205)
( 21,181)( 22,182)( 23,184)( 24,183)( 25,186)( 26,185)( 27,187)( 28,188)
( 29,196)( 30,195)( 31,193)( 32,194)( 33,191)( 34,192)( 35,190)( 36,189)
( 37,165)( 38,166)( 39,168)( 40,167)( 41,170)( 42,169)( 43,171)( 44,172)
( 45,180)( 46,179)( 47,177)( 48,178)( 49,175)( 50,176)( 51,174)( 52,173)
( 53,229)( 54,230)( 55,232)( 56,231)( 57,234)( 58,233)( 59,235)( 60,236)
( 61,244)( 62,243)( 63,241)( 64,242)( 65,239)( 66,240)( 67,238)( 68,237)
( 69,213)( 70,214)( 71,216)( 72,215)( 73,218)( 74,217)( 75,219)( 76,220)
( 77,228)( 78,227)( 79,225)( 80,226)( 81,223)( 82,224)( 83,222)( 84,221)
( 85,277)( 86,278)( 87,280)( 88,279)( 89,282)( 90,281)( 91,283)( 92,284)
( 93,292)( 94,291)( 95,289)( 96,290)( 97,287)( 98,288)( 99,286)(100,285)
(101,261)(102,262)(103,264)(104,263)(105,266)(106,265)(107,267)(108,268)
(109,276)(110,275)(111,273)(112,274)(113,271)(114,272)(115,270)(116,269)
(117,245)(118,246)(119,248)(120,247)(121,250)(122,249)(123,251)(124,252)
(125,260)(126,259)(127,257)(128,258)(129,255)(130,256)(131,254)(132,253)
(133,309)(134,310)(135,312)(136,311)(137,314)(138,313)(139,315)(140,316)
(141,324)(142,323)(143,321)(144,322)(145,319)(146,320)(147,318)(148,317)
(149,293)(150,294)(151,296)(152,295)(153,298)(154,297)(155,299)(156,300)
(157,308)(158,307)(159,305)(160,306)(161,303)(162,304)(163,302)(164,301);;
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, 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(324)!(1,2);
s1 := Sym(324)!(3,4);
s2 := Sym(324)!( 5, 86)( 6, 85)( 7, 88)( 8, 87)( 9, 90)( 10, 89)( 11, 92)
( 12, 91)( 13, 94)( 14, 93)( 15, 96)( 16, 95)( 17, 98)( 18, 97)( 19,100)
( 20, 99)( 21,102)( 22,101)( 23,104)( 24,103)( 25,106)( 26,105)( 27,108)
( 28,107)( 29,110)( 30,109)( 31,112)( 32,111)( 33,114)( 34,113)( 35,116)
( 36,115)( 37,118)( 38,117)( 39,120)( 40,119)( 41,122)( 42,121)( 43,124)
( 44,123)( 45,126)( 46,125)( 47,128)( 48,127)( 49,130)( 50,129)( 51,132)
( 52,131)( 53,134)( 54,133)( 55,136)( 56,135)( 57,138)( 58,137)( 59,140)
( 60,139)( 61,142)( 62,141)( 63,144)( 64,143)( 65,146)( 66,145)( 67,148)
( 68,147)( 69,150)( 70,149)( 71,152)( 72,151)( 73,154)( 74,153)( 75,156)
( 76,155)( 77,158)( 78,157)( 79,160)( 80,159)( 81,162)( 82,161)( 83,164)
( 84,163)(165,246)(166,245)(167,248)(168,247)(169,250)(170,249)(171,252)
(172,251)(173,254)(174,253)(175,256)(176,255)(177,258)(178,257)(179,260)
(180,259)(181,262)(182,261)(183,264)(184,263)(185,266)(186,265)(187,268)
(188,267)(189,270)(190,269)(191,272)(192,271)(193,274)(194,273)(195,276)
(196,275)(197,278)(198,277)(199,280)(200,279)(201,282)(202,281)(203,284)
(204,283)(205,286)(206,285)(207,288)(208,287)(209,290)(210,289)(211,292)
(212,291)(213,294)(214,293)(215,296)(216,295)(217,298)(218,297)(219,300)
(220,299)(221,302)(222,301)(223,304)(224,303)(225,306)(226,305)(227,308)
(228,307)(229,310)(230,309)(231,312)(232,311)(233,314)(234,313)(235,316)
(236,315)(237,318)(238,317)(239,320)(240,319)(241,322)(242,321)(243,324)
(244,323);
s3 := 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);
s4 := Sym(324)!( 5,197)( 6,198)( 7,200)( 8,199)( 9,202)( 10,201)( 11,203)
( 12,204)( 13,212)( 14,211)( 15,209)( 16,210)( 17,207)( 18,208)( 19,206)
( 20,205)( 21,181)( 22,182)( 23,184)( 24,183)( 25,186)( 26,185)( 27,187)
( 28,188)( 29,196)( 30,195)( 31,193)( 32,194)( 33,191)( 34,192)( 35,190)
( 36,189)( 37,165)( 38,166)( 39,168)( 40,167)( 41,170)( 42,169)( 43,171)
( 44,172)( 45,180)( 46,179)( 47,177)( 48,178)( 49,175)( 50,176)( 51,174)
( 52,173)( 53,229)( 54,230)( 55,232)( 56,231)( 57,234)( 58,233)( 59,235)
( 60,236)( 61,244)( 62,243)( 63,241)( 64,242)( 65,239)( 66,240)( 67,238)
( 68,237)( 69,213)( 70,214)( 71,216)( 72,215)( 73,218)( 74,217)( 75,219)
( 76,220)( 77,228)( 78,227)( 79,225)( 80,226)( 81,223)( 82,224)( 83,222)
( 84,221)( 85,277)( 86,278)( 87,280)( 88,279)( 89,282)( 90,281)( 91,283)
( 92,284)( 93,292)( 94,291)( 95,289)( 96,290)( 97,287)( 98,288)( 99,286)
(100,285)(101,261)(102,262)(103,264)(104,263)(105,266)(106,265)(107,267)
(108,268)(109,276)(110,275)(111,273)(112,274)(113,271)(114,272)(115,270)
(116,269)(117,245)(118,246)(119,248)(120,247)(121,250)(122,249)(123,251)
(124,252)(125,260)(126,259)(127,257)(128,258)(129,255)(130,256)(131,254)
(132,253)(133,309)(134,310)(135,312)(136,311)(137,314)(138,313)(139,315)
(140,316)(141,324)(142,323)(143,321)(144,322)(145,319)(146,320)(147,318)
(148,317)(149,293)(150,294)(151,296)(152,295)(153,298)(154,297)(155,299)
(156,300)(157,308)(158,307)(159,305)(160,306)(161,303)(162,304)(163,302)
(164,301);
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,
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