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