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