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