Polytope of Type {2,5,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,5,10}*1280
if this polytope has a name.
Group : SmallGroup(1280,1116450)
Rank : 4
Schlafli Type : {2,5,10}
Number of vertices, edges, etc : 2, 32, 160, 64
Order of s₀s₁s₂s₃ : 8
Order of s₀s₁s₂s₃s₂s₁ : 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 : {2,5,5}*640, {2,5,10}*640a, {2,5,10}*640b
   4-fold quotients : {2,5,5}*320
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  5, 30)(  6, 29)(  7, 17)(  8, 18)(  9, 23)( 10, 24)( 11, 20)( 12, 19)
( 13, 14)( 15, 34)( 16, 33)( 25, 31)( 26, 32)( 27, 28)( 35,131)( 36,132)
( 37,158)( 38,157)( 39,145)( 40,146)( 41,151)( 42,152)( 43,148)( 44,147)
( 45,142)( 46,141)( 47,162)( 48,161)( 49,135)( 50,136)( 51,140)( 52,139)
( 53,149)( 54,150)( 55,137)( 56,138)( 57,159)( 58,160)( 59,156)( 60,155)
( 61,134)( 62,133)( 63,153)( 64,154)( 65,144)( 66,143)( 67, 99)( 68,100)
( 69,126)( 70,125)( 71,113)( 72,114)( 73,119)( 74,120)( 75,116)( 76,115)
( 77,110)( 78,109)( 79,130)( 80,129)( 81,103)( 82,104)( 83,108)( 84,107)
( 85,117)( 86,118)( 87,105)( 88,106)( 89,127)( 90,128)( 91,124)( 92,123)
( 93,102)( 94,101)( 95,121)( 96,122)( 97,112)( 98,111)(165,190)(166,189)
(167,177)(168,178)(169,183)(170,184)(171,180)(172,179)(173,174)(175,194)
(176,193)(185,191)(186,192)(187,188)(195,291)(196,292)(197,318)(198,317)
(199,305)(200,306)(201,311)(202,312)(203,308)(204,307)(205,302)(206,301)
(207,322)(208,321)(209,295)(210,296)(211,300)(212,299)(213,309)(214,310)
(215,297)(216,298)(217,319)(218,320)(219,316)(220,315)(221,294)(222,293)
(223,313)(224,314)(225,304)(226,303)(227,259)(228,260)(229,286)(230,285)
(231,273)(232,274)(233,279)(234,280)(235,276)(236,275)(237,270)(238,269)
(239,290)(240,289)(241,263)(242,264)(243,268)(244,267)(245,277)(246,278)
(247,265)(248,266)(249,287)(250,288)(251,284)(252,283)(253,262)(254,261)
(255,281)(256,282)(257,272)(258,271);;
s2 := (  3, 35)(  4, 36)(  5, 57)(  6, 58)(  7, 59)(  8, 60)(  9, 49)( 10, 50)
( 11, 44)( 12, 43)( 13, 65)( 14, 66)( 15, 52)( 16, 51)( 17, 41)( 18, 42)
( 19, 48)( 20, 47)( 21, 61)( 22, 62)( 23, 56)( 24, 55)( 25, 37)( 26, 38)
( 27, 39)( 28, 40)( 29, 53)( 30, 54)( 31, 63)( 32, 64)( 33, 45)( 34, 46)
( 67,131)( 68,132)( 69,153)( 70,154)( 71,155)( 72,156)( 73,145)( 74,146)
( 75,140)( 76,139)( 77,161)( 78,162)( 79,148)( 80,147)( 81,137)( 82,138)
( 83,144)( 84,143)( 85,157)( 86,158)( 87,152)( 88,151)( 89,133)( 90,134)
( 91,135)( 92,136)( 93,149)( 94,150)( 95,159)( 96,160)( 97,141)( 98,142)
(101,121)(102,122)(103,123)(104,124)(105,113)(106,114)(107,108)(109,129)
(110,130)(111,116)(112,115)(117,125)(118,126)(119,120)(163,195)(164,196)
(165,217)(166,218)(167,219)(168,220)(169,209)(170,210)(171,204)(172,203)
(173,225)(174,226)(175,212)(176,211)(177,201)(178,202)(179,208)(180,207)
(181,221)(182,222)(183,216)(184,215)(185,197)(186,198)(187,199)(188,200)
(189,213)(190,214)(191,223)(192,224)(193,205)(194,206)(227,291)(228,292)
(229,313)(230,314)(231,315)(232,316)(233,305)(234,306)(235,300)(236,299)
(237,321)(238,322)(239,308)(240,307)(241,297)(242,298)(243,304)(244,303)
(245,317)(246,318)(247,312)(248,311)(249,293)(250,294)(251,295)(252,296)
(253,309)(254,310)(255,319)(256,320)(257,301)(258,302)(261,281)(262,282)
(263,283)(264,284)(265,273)(266,274)(267,268)(269,289)(270,290)(271,276)
(272,275)(277,285)(278,286)(279,280);;
s3 := (  3,181)(  4,182)(  5,171)(  6,172)(  7,192)(  8,191)(  9,169)( 10,170)
( 11,165)( 12,166)( 13,188)( 14,187)( 15,176)( 16,175)( 17,186)( 18,185)
( 19,189)( 20,190)( 21,163)( 22,164)( 23,183)( 24,184)( 25,178)( 26,177)
( 27,174)( 28,173)( 29,179)( 30,180)( 31,168)( 32,167)( 33,194)( 34,193)
( 35,309)( 36,310)( 37,299)( 38,300)( 39,320)( 40,319)( 41,297)( 42,298)
( 43,293)( 44,294)( 45,316)( 46,315)( 47,304)( 48,303)( 49,314)( 50,313)
( 51,317)( 52,318)( 53,291)( 54,292)( 55,311)( 56,312)( 57,306)( 58,305)
( 59,302)( 60,301)( 61,307)( 62,308)( 63,296)( 64,295)( 65,322)( 66,321)
( 67,277)( 68,278)( 69,267)( 70,268)( 71,288)( 72,287)( 73,265)( 74,266)
( 75,261)( 76,262)( 77,284)( 78,283)( 79,272)( 80,271)( 81,282)( 82,281)
( 83,285)( 84,286)( 85,259)( 86,260)( 87,279)( 88,280)( 89,274)( 90,273)
( 91,270)( 92,269)( 93,275)( 94,276)( 95,264)( 96,263)( 97,290)( 98,289)
( 99,245)(100,246)(101,235)(102,236)(103,256)(104,255)(105,233)(106,234)
(107,229)(108,230)(109,252)(110,251)(111,240)(112,239)(113,250)(114,249)
(115,253)(116,254)(117,227)(118,228)(119,247)(120,248)(121,242)(122,241)
(123,238)(124,237)(125,243)(126,244)(127,232)(128,231)(129,258)(130,257)
(131,213)(132,214)(133,203)(134,204)(135,224)(136,223)(137,201)(138,202)
(139,197)(140,198)(141,220)(142,219)(143,208)(144,207)(145,218)(146,217)
(147,221)(148,222)(149,195)(150,196)(151,215)(152,216)(153,210)(154,209)
(155,206)(156,205)(157,211)(158,212)(159,200)(160,199)(161,226)(162,225);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(322)!(1,2);
s1 := Sym(322)!(  5, 30)(  6, 29)(  7, 17)(  8, 18)(  9, 23)( 10, 24)( 11, 20)
( 12, 19)( 13, 14)( 15, 34)( 16, 33)( 25, 31)( 26, 32)( 27, 28)( 35,131)
( 36,132)( 37,158)( 38,157)( 39,145)( 40,146)( 41,151)( 42,152)( 43,148)
( 44,147)( 45,142)( 46,141)( 47,162)( 48,161)( 49,135)( 50,136)( 51,140)
( 52,139)( 53,149)( 54,150)( 55,137)( 56,138)( 57,159)( 58,160)( 59,156)
( 60,155)( 61,134)( 62,133)( 63,153)( 64,154)( 65,144)( 66,143)( 67, 99)
( 68,100)( 69,126)( 70,125)( 71,113)( 72,114)( 73,119)( 74,120)( 75,116)
( 76,115)( 77,110)( 78,109)( 79,130)( 80,129)( 81,103)( 82,104)( 83,108)
( 84,107)( 85,117)( 86,118)( 87,105)( 88,106)( 89,127)( 90,128)( 91,124)
( 92,123)( 93,102)( 94,101)( 95,121)( 96,122)( 97,112)( 98,111)(165,190)
(166,189)(167,177)(168,178)(169,183)(170,184)(171,180)(172,179)(173,174)
(175,194)(176,193)(185,191)(186,192)(187,188)(195,291)(196,292)(197,318)
(198,317)(199,305)(200,306)(201,311)(202,312)(203,308)(204,307)(205,302)
(206,301)(207,322)(208,321)(209,295)(210,296)(211,300)(212,299)(213,309)
(214,310)(215,297)(216,298)(217,319)(218,320)(219,316)(220,315)(221,294)
(222,293)(223,313)(224,314)(225,304)(226,303)(227,259)(228,260)(229,286)
(230,285)(231,273)(232,274)(233,279)(234,280)(235,276)(236,275)(237,270)
(238,269)(239,290)(240,289)(241,263)(242,264)(243,268)(244,267)(245,277)
(246,278)(247,265)(248,266)(249,287)(250,288)(251,284)(252,283)(253,262)
(254,261)(255,281)(256,282)(257,272)(258,271);
s2 := Sym(322)!(  3, 35)(  4, 36)(  5, 57)(  6, 58)(  7, 59)(  8, 60)(  9, 49)
( 10, 50)( 11, 44)( 12, 43)( 13, 65)( 14, 66)( 15, 52)( 16, 51)( 17, 41)
( 18, 42)( 19, 48)( 20, 47)( 21, 61)( 22, 62)( 23, 56)( 24, 55)( 25, 37)
( 26, 38)( 27, 39)( 28, 40)( 29, 53)( 30, 54)( 31, 63)( 32, 64)( 33, 45)
( 34, 46)( 67,131)( 68,132)( 69,153)( 70,154)( 71,155)( 72,156)( 73,145)
( 74,146)( 75,140)( 76,139)( 77,161)( 78,162)( 79,148)( 80,147)( 81,137)
( 82,138)( 83,144)( 84,143)( 85,157)( 86,158)( 87,152)( 88,151)( 89,133)
( 90,134)( 91,135)( 92,136)( 93,149)( 94,150)( 95,159)( 96,160)( 97,141)
( 98,142)(101,121)(102,122)(103,123)(104,124)(105,113)(106,114)(107,108)
(109,129)(110,130)(111,116)(112,115)(117,125)(118,126)(119,120)(163,195)
(164,196)(165,217)(166,218)(167,219)(168,220)(169,209)(170,210)(171,204)
(172,203)(173,225)(174,226)(175,212)(176,211)(177,201)(178,202)(179,208)
(180,207)(181,221)(182,222)(183,216)(184,215)(185,197)(186,198)(187,199)
(188,200)(189,213)(190,214)(191,223)(192,224)(193,205)(194,206)(227,291)
(228,292)(229,313)(230,314)(231,315)(232,316)(233,305)(234,306)(235,300)
(236,299)(237,321)(238,322)(239,308)(240,307)(241,297)(242,298)(243,304)
(244,303)(245,317)(246,318)(247,312)(248,311)(249,293)(250,294)(251,295)
(252,296)(253,309)(254,310)(255,319)(256,320)(257,301)(258,302)(261,281)
(262,282)(263,283)(264,284)(265,273)(266,274)(267,268)(269,289)(270,290)
(271,276)(272,275)(277,285)(278,286)(279,280);
s3 := Sym(322)!(  3,181)(  4,182)(  5,171)(  6,172)(  7,192)(  8,191)(  9,169)
( 10,170)( 11,165)( 12,166)( 13,188)( 14,187)( 15,176)( 16,175)( 17,186)
( 18,185)( 19,189)( 20,190)( 21,163)( 22,164)( 23,183)( 24,184)( 25,178)
( 26,177)( 27,174)( 28,173)( 29,179)( 30,180)( 31,168)( 32,167)( 33,194)
( 34,193)( 35,309)( 36,310)( 37,299)( 38,300)( 39,320)( 40,319)( 41,297)
( 42,298)( 43,293)( 44,294)( 45,316)( 46,315)( 47,304)( 48,303)( 49,314)
( 50,313)( 51,317)( 52,318)( 53,291)( 54,292)( 55,311)( 56,312)( 57,306)
( 58,305)( 59,302)( 60,301)( 61,307)( 62,308)( 63,296)( 64,295)( 65,322)
( 66,321)( 67,277)( 68,278)( 69,267)( 70,268)( 71,288)( 72,287)( 73,265)
( 74,266)( 75,261)( 76,262)( 77,284)( 78,283)( 79,272)( 80,271)( 81,282)
( 82,281)( 83,285)( 84,286)( 85,259)( 86,260)( 87,279)( 88,280)( 89,274)
( 90,273)( 91,270)( 92,269)( 93,275)( 94,276)( 95,264)( 96,263)( 97,290)
( 98,289)( 99,245)(100,246)(101,235)(102,236)(103,256)(104,255)(105,233)
(106,234)(107,229)(108,230)(109,252)(110,251)(111,240)(112,239)(113,250)
(114,249)(115,253)(116,254)(117,227)(118,228)(119,247)(120,248)(121,242)
(122,241)(123,238)(124,237)(125,243)(126,244)(127,232)(128,231)(129,258)
(130,257)(131,213)(132,214)(133,203)(134,204)(135,224)(136,223)(137,201)
(138,202)(139,197)(140,198)(141,220)(142,219)(143,208)(144,207)(145,218)
(146,217)(147,221)(148,222)(149,195)(150,196)(151,215)(152,216)(153,210)
(154,209)(155,206)(156,205)(157,211)(158,212)(159,200)(160,199)(161,226)
(162,225);
poly := sub<Sym(322)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2 >;

to this polytope