Polytope of Type {32,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {32,10}*640
Also Known As : {32,10|2}. if this polytope has another name.
Group : SmallGroup(640,2250)
Rank : 3
Schlafli Type : {32,10}
Number of vertices, edges, etc : 32, 160, 10
Order of s0s1s2 : 160
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{32,10,2} of size 1280
Vertex Figure Of :
{2,32,10} of size 1280
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {16,10}*320
4-fold quotients : {8,10}*160
5-fold quotients : {32,2}*128
8-fold quotients : {4,10}*80
10-fold quotients : {16,2}*64
16-fold quotients : {2,10}*40
20-fold quotients : {8,2}*32
32-fold quotients : {2,5}*20
40-fold quotients : {4,2}*16
80-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {32,20}*1280a, {64,10}*1280
3-fold covers : {32,30}*1920, {96,10}*1920
Permutation Representation (GAP) :
s0 := ( 11, 16)( 12, 17)( 13, 18)( 14, 19)( 15, 20)( 21, 31)( 22, 32)( 23, 33)
( 24, 34)( 25, 35)( 26, 36)( 27, 37)( 28, 38)( 29, 39)( 30, 40)( 41, 61)
( 42, 62)( 43, 63)( 44, 64)( 45, 65)( 46, 66)( 47, 67)( 48, 68)( 49, 69)
( 50, 70)( 51, 76)( 52, 77)( 53, 78)( 54, 79)( 55, 80)( 56, 71)( 57, 72)
( 58, 73)( 59, 74)( 60, 75)( 91, 96)( 92, 97)( 93, 98)( 94, 99)( 95,100)
(101,111)(102,112)(103,113)(104,114)(105,115)(106,116)(107,117)(108,118)
(109,119)(110,120)(121,141)(122,142)(123,143)(124,144)(125,145)(126,146)
(127,147)(128,148)(129,149)(130,150)(131,156)(132,157)(133,158)(134,159)
(135,160)(136,151)(137,152)(138,153)(139,154)(140,155)(161,201)(162,202)
(163,203)(164,204)(165,205)(166,206)(167,207)(168,208)(169,209)(170,210)
(171,216)(172,217)(173,218)(174,219)(175,220)(176,211)(177,212)(178,213)
(179,214)(180,215)(181,231)(182,232)(183,233)(184,234)(185,235)(186,236)
(187,237)(188,238)(189,239)(190,240)(191,221)(192,222)(193,223)(194,224)
(195,225)(196,226)(197,227)(198,228)(199,229)(200,230)(241,281)(242,282)
(243,283)(244,284)(245,285)(246,286)(247,287)(248,288)(249,289)(250,290)
(251,296)(252,297)(253,298)(254,299)(255,300)(256,291)(257,292)(258,293)
(259,294)(260,295)(261,311)(262,312)(263,313)(264,314)(265,315)(266,316)
(267,317)(268,318)(269,319)(270,320)(271,301)(272,302)(273,303)(274,304)
(275,305)(276,306)(277,307)(278,308)(279,309)(280,310);;
s1 := ( 1,241)( 2,245)( 3,244)( 4,243)( 5,242)( 6,246)( 7,250)( 8,249)
( 9,248)( 10,247)( 11,256)( 12,260)( 13,259)( 14,258)( 15,257)( 16,251)
( 17,255)( 18,254)( 19,253)( 20,252)( 21,271)( 22,275)( 23,274)( 24,273)
( 25,272)( 26,276)( 27,280)( 28,279)( 29,278)( 30,277)( 31,261)( 32,265)
( 33,264)( 34,263)( 35,262)( 36,266)( 37,270)( 38,269)( 39,268)( 40,267)
( 41,301)( 42,305)( 43,304)( 44,303)( 45,302)( 46,306)( 47,310)( 48,309)
( 49,308)( 50,307)( 51,316)( 52,320)( 53,319)( 54,318)( 55,317)( 56,311)
( 57,315)( 58,314)( 59,313)( 60,312)( 61,281)( 62,285)( 63,284)( 64,283)
( 65,282)( 66,286)( 67,290)( 68,289)( 69,288)( 70,287)( 71,296)( 72,300)
( 73,299)( 74,298)( 75,297)( 76,291)( 77,295)( 78,294)( 79,293)( 80,292)
( 81,161)( 82,165)( 83,164)( 84,163)( 85,162)( 86,166)( 87,170)( 88,169)
( 89,168)( 90,167)( 91,176)( 92,180)( 93,179)( 94,178)( 95,177)( 96,171)
( 97,175)( 98,174)( 99,173)(100,172)(101,191)(102,195)(103,194)(104,193)
(105,192)(106,196)(107,200)(108,199)(109,198)(110,197)(111,181)(112,185)
(113,184)(114,183)(115,182)(116,186)(117,190)(118,189)(119,188)(120,187)
(121,221)(122,225)(123,224)(124,223)(125,222)(126,226)(127,230)(128,229)
(129,228)(130,227)(131,236)(132,240)(133,239)(134,238)(135,237)(136,231)
(137,235)(138,234)(139,233)(140,232)(141,201)(142,205)(143,204)(144,203)
(145,202)(146,206)(147,210)(148,209)(149,208)(150,207)(151,216)(152,220)
(153,219)(154,218)(155,217)(156,211)(157,215)(158,214)(159,213)(160,212);;
s2 := ( 1, 82)( 2, 81)( 3, 85)( 4, 84)( 5, 83)( 6, 87)( 7, 86)( 8, 90)
( 9, 89)( 10, 88)( 11, 92)( 12, 91)( 13, 95)( 14, 94)( 15, 93)( 16, 97)
( 17, 96)( 18,100)( 19, 99)( 20, 98)( 21,102)( 22,101)( 23,105)( 24,104)
( 25,103)( 26,107)( 27,106)( 28,110)( 29,109)( 30,108)( 31,112)( 32,111)
( 33,115)( 34,114)( 35,113)( 36,117)( 37,116)( 38,120)( 39,119)( 40,118)
( 41,122)( 42,121)( 43,125)( 44,124)( 45,123)( 46,127)( 47,126)( 48,130)
( 49,129)( 50,128)( 51,132)( 52,131)( 53,135)( 54,134)( 55,133)( 56,137)
( 57,136)( 58,140)( 59,139)( 60,138)( 61,142)( 62,141)( 63,145)( 64,144)
( 65,143)( 66,147)( 67,146)( 68,150)( 69,149)( 70,148)( 71,152)( 72,151)
( 73,155)( 74,154)( 75,153)( 76,157)( 77,156)( 78,160)( 79,159)( 80,158)
(161,242)(162,241)(163,245)(164,244)(165,243)(166,247)(167,246)(168,250)
(169,249)(170,248)(171,252)(172,251)(173,255)(174,254)(175,253)(176,257)
(177,256)(178,260)(179,259)(180,258)(181,262)(182,261)(183,265)(184,264)
(185,263)(186,267)(187,266)(188,270)(189,269)(190,268)(191,272)(192,271)
(193,275)(194,274)(195,273)(196,277)(197,276)(198,280)(199,279)(200,278)
(201,282)(202,281)(203,285)(204,284)(205,283)(206,287)(207,286)(208,290)
(209,289)(210,288)(211,292)(212,291)(213,295)(214,294)(215,293)(216,297)
(217,296)(218,300)(219,299)(220,298)(221,302)(222,301)(223,305)(224,304)
(225,303)(226,307)(227,306)(228,310)(229,309)(230,308)(231,312)(232,311)
(233,315)(234,314)(235,313)(236,317)(237,316)(238,320)(239,319)(240,318);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(320)!( 11, 16)( 12, 17)( 13, 18)( 14, 19)( 15, 20)( 21, 31)( 22, 32)
( 23, 33)( 24, 34)( 25, 35)( 26, 36)( 27, 37)( 28, 38)( 29, 39)( 30, 40)
( 41, 61)( 42, 62)( 43, 63)( 44, 64)( 45, 65)( 46, 66)( 47, 67)( 48, 68)
( 49, 69)( 50, 70)( 51, 76)( 52, 77)( 53, 78)( 54, 79)( 55, 80)( 56, 71)
( 57, 72)( 58, 73)( 59, 74)( 60, 75)( 91, 96)( 92, 97)( 93, 98)( 94, 99)
( 95,100)(101,111)(102,112)(103,113)(104,114)(105,115)(106,116)(107,117)
(108,118)(109,119)(110,120)(121,141)(122,142)(123,143)(124,144)(125,145)
(126,146)(127,147)(128,148)(129,149)(130,150)(131,156)(132,157)(133,158)
(134,159)(135,160)(136,151)(137,152)(138,153)(139,154)(140,155)(161,201)
(162,202)(163,203)(164,204)(165,205)(166,206)(167,207)(168,208)(169,209)
(170,210)(171,216)(172,217)(173,218)(174,219)(175,220)(176,211)(177,212)
(178,213)(179,214)(180,215)(181,231)(182,232)(183,233)(184,234)(185,235)
(186,236)(187,237)(188,238)(189,239)(190,240)(191,221)(192,222)(193,223)
(194,224)(195,225)(196,226)(197,227)(198,228)(199,229)(200,230)(241,281)
(242,282)(243,283)(244,284)(245,285)(246,286)(247,287)(248,288)(249,289)
(250,290)(251,296)(252,297)(253,298)(254,299)(255,300)(256,291)(257,292)
(258,293)(259,294)(260,295)(261,311)(262,312)(263,313)(264,314)(265,315)
(266,316)(267,317)(268,318)(269,319)(270,320)(271,301)(272,302)(273,303)
(274,304)(275,305)(276,306)(277,307)(278,308)(279,309)(280,310);
s1 := Sym(320)!( 1,241)( 2,245)( 3,244)( 4,243)( 5,242)( 6,246)( 7,250)
( 8,249)( 9,248)( 10,247)( 11,256)( 12,260)( 13,259)( 14,258)( 15,257)
( 16,251)( 17,255)( 18,254)( 19,253)( 20,252)( 21,271)( 22,275)( 23,274)
( 24,273)( 25,272)( 26,276)( 27,280)( 28,279)( 29,278)( 30,277)( 31,261)
( 32,265)( 33,264)( 34,263)( 35,262)( 36,266)( 37,270)( 38,269)( 39,268)
( 40,267)( 41,301)( 42,305)( 43,304)( 44,303)( 45,302)( 46,306)( 47,310)
( 48,309)( 49,308)( 50,307)( 51,316)( 52,320)( 53,319)( 54,318)( 55,317)
( 56,311)( 57,315)( 58,314)( 59,313)( 60,312)( 61,281)( 62,285)( 63,284)
( 64,283)( 65,282)( 66,286)( 67,290)( 68,289)( 69,288)( 70,287)( 71,296)
( 72,300)( 73,299)( 74,298)( 75,297)( 76,291)( 77,295)( 78,294)( 79,293)
( 80,292)( 81,161)( 82,165)( 83,164)( 84,163)( 85,162)( 86,166)( 87,170)
( 88,169)( 89,168)( 90,167)( 91,176)( 92,180)( 93,179)( 94,178)( 95,177)
( 96,171)( 97,175)( 98,174)( 99,173)(100,172)(101,191)(102,195)(103,194)
(104,193)(105,192)(106,196)(107,200)(108,199)(109,198)(110,197)(111,181)
(112,185)(113,184)(114,183)(115,182)(116,186)(117,190)(118,189)(119,188)
(120,187)(121,221)(122,225)(123,224)(124,223)(125,222)(126,226)(127,230)
(128,229)(129,228)(130,227)(131,236)(132,240)(133,239)(134,238)(135,237)
(136,231)(137,235)(138,234)(139,233)(140,232)(141,201)(142,205)(143,204)
(144,203)(145,202)(146,206)(147,210)(148,209)(149,208)(150,207)(151,216)
(152,220)(153,219)(154,218)(155,217)(156,211)(157,215)(158,214)(159,213)
(160,212);
s2 := Sym(320)!( 1, 82)( 2, 81)( 3, 85)( 4, 84)( 5, 83)( 6, 87)( 7, 86)
( 8, 90)( 9, 89)( 10, 88)( 11, 92)( 12, 91)( 13, 95)( 14, 94)( 15, 93)
( 16, 97)( 17, 96)( 18,100)( 19, 99)( 20, 98)( 21,102)( 22,101)( 23,105)
( 24,104)( 25,103)( 26,107)( 27,106)( 28,110)( 29,109)( 30,108)( 31,112)
( 32,111)( 33,115)( 34,114)( 35,113)( 36,117)( 37,116)( 38,120)( 39,119)
( 40,118)( 41,122)( 42,121)( 43,125)( 44,124)( 45,123)( 46,127)( 47,126)
( 48,130)( 49,129)( 50,128)( 51,132)( 52,131)( 53,135)( 54,134)( 55,133)
( 56,137)( 57,136)( 58,140)( 59,139)( 60,138)( 61,142)( 62,141)( 63,145)
( 64,144)( 65,143)( 66,147)( 67,146)( 68,150)( 69,149)( 70,148)( 71,152)
( 72,151)( 73,155)( 74,154)( 75,153)( 76,157)( 77,156)( 78,160)( 79,159)
( 80,158)(161,242)(162,241)(163,245)(164,244)(165,243)(166,247)(167,246)
(168,250)(169,249)(170,248)(171,252)(172,251)(173,255)(174,254)(175,253)
(176,257)(177,256)(178,260)(179,259)(180,258)(181,262)(182,261)(183,265)
(184,264)(185,263)(186,267)(187,266)(188,270)(189,269)(190,268)(191,272)
(192,271)(193,275)(194,274)(195,273)(196,277)(197,276)(198,280)(199,279)
(200,278)(201,282)(202,281)(203,285)(204,284)(205,283)(206,287)(207,286)
(208,290)(209,289)(210,288)(211,292)(212,291)(213,295)(214,294)(215,293)
(216,297)(217,296)(218,300)(219,299)(220,298)(221,302)(222,301)(223,305)
(224,304)(225,303)(226,307)(227,306)(228,310)(229,309)(230,308)(231,312)
(232,311)(233,315)(234,314)(235,313)(236,317)(237,316)(238,320)(239,319)
(240,318);
poly := sub<Sym(320)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope