Polytope of Type {2,10,32}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,32}*1280
if this polytope has a name.
Group : SmallGroup(1280,327682)
Rank : 4
Schlafli Type : {2,10,32}
Number of vertices, edges, etc : 2, 10, 160, 32
Order of s0s1s2s3 : 160
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 : {2,10,16}*640
4-fold quotients : {2,10,8}*320
5-fold quotients : {2,2,32}*256
8-fold quotients : {2,10,4}*160
10-fold quotients : {2,2,16}*128
16-fold quotients : {2,10,2}*80
20-fold quotients : {2,2,8}*64
32-fold quotients : {2,5,2}*40
40-fold quotients : {2,2,4}*32
80-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3, 83)( 4, 87)( 5, 86)( 6, 85)( 7, 84)( 8, 88)( 9, 92)( 10, 91)
( 11, 90)( 12, 89)( 13, 93)( 14, 97)( 15, 96)( 16, 95)( 17, 94)( 18, 98)
( 19,102)( 20,101)( 21,100)( 22, 99)( 23,103)( 24,107)( 25,106)( 26,105)
( 27,104)( 28,108)( 29,112)( 30,111)( 31,110)( 32,109)( 33,113)( 34,117)
( 35,116)( 36,115)( 37,114)( 38,118)( 39,122)( 40,121)( 41,120)( 42,119)
( 43,123)( 44,127)( 45,126)( 46,125)( 47,124)( 48,128)( 49,132)( 50,131)
( 51,130)( 52,129)( 53,133)( 54,137)( 55,136)( 56,135)( 57,134)( 58,138)
( 59,142)( 60,141)( 61,140)( 62,139)( 63,143)( 64,147)( 65,146)( 66,145)
( 67,144)( 68,148)( 69,152)( 70,151)( 71,150)( 72,149)( 73,153)( 74,157)
( 75,156)( 76,155)( 77,154)( 78,158)( 79,162)( 80,161)( 81,160)( 82,159)
(163,243)(164,247)(165,246)(166,245)(167,244)(168,248)(169,252)(170,251)
(171,250)(172,249)(173,253)(174,257)(175,256)(176,255)(177,254)(178,258)
(179,262)(180,261)(181,260)(182,259)(183,263)(184,267)(185,266)(186,265)
(187,264)(188,268)(189,272)(190,271)(191,270)(192,269)(193,273)(194,277)
(195,276)(196,275)(197,274)(198,278)(199,282)(200,281)(201,280)(202,279)
(203,283)(204,287)(205,286)(206,285)(207,284)(208,288)(209,292)(210,291)
(211,290)(212,289)(213,293)(214,297)(215,296)(216,295)(217,294)(218,298)
(219,302)(220,301)(221,300)(222,299)(223,303)(224,307)(225,306)(226,305)
(227,304)(228,308)(229,312)(230,311)(231,310)(232,309)(233,313)(234,317)
(235,316)(236,315)(237,314)(238,318)(239,322)(240,321)(241,320)(242,319);;
s2 := ( 3, 84)( 4, 83)( 5, 87)( 6, 86)( 7, 85)( 8, 89)( 9, 88)( 10, 92)
( 11, 91)( 12, 90)( 13, 99)( 14, 98)( 15,102)( 16,101)( 17,100)( 18, 94)
( 19, 93)( 20, 97)( 21, 96)( 22, 95)( 23,114)( 24,113)( 25,117)( 26,116)
( 27,115)( 28,119)( 29,118)( 30,122)( 31,121)( 32,120)( 33,104)( 34,103)
( 35,107)( 36,106)( 37,105)( 38,109)( 39,108)( 40,112)( 41,111)( 42,110)
( 43,144)( 44,143)( 45,147)( 46,146)( 47,145)( 48,149)( 49,148)( 50,152)
( 51,151)( 52,150)( 53,159)( 54,158)( 55,162)( 56,161)( 57,160)( 58,154)
( 59,153)( 60,157)( 61,156)( 62,155)( 63,124)( 64,123)( 65,127)( 66,126)
( 67,125)( 68,129)( 69,128)( 70,132)( 71,131)( 72,130)( 73,139)( 74,138)
( 75,142)( 76,141)( 77,140)( 78,134)( 79,133)( 80,137)( 81,136)( 82,135)
(163,284)(164,283)(165,287)(166,286)(167,285)(168,289)(169,288)(170,292)
(171,291)(172,290)(173,299)(174,298)(175,302)(176,301)(177,300)(178,294)
(179,293)(180,297)(181,296)(182,295)(183,314)(184,313)(185,317)(186,316)
(187,315)(188,319)(189,318)(190,322)(191,321)(192,320)(193,304)(194,303)
(195,307)(196,306)(197,305)(198,309)(199,308)(200,312)(201,311)(202,310)
(203,244)(204,243)(205,247)(206,246)(207,245)(208,249)(209,248)(210,252)
(211,251)(212,250)(213,259)(214,258)(215,262)(216,261)(217,260)(218,254)
(219,253)(220,257)(221,256)(222,255)(223,274)(224,273)(225,277)(226,276)
(227,275)(228,279)(229,278)(230,282)(231,281)(232,280)(233,264)(234,263)
(235,267)(236,266)(237,265)(238,269)(239,268)(240,272)(241,271)(242,270);;
s3 := ( 3,163)( 4,164)( 5,165)( 6,166)( 7,167)( 8,168)( 9,169)( 10,170)
( 11,171)( 12,172)( 13,178)( 14,179)( 15,180)( 16,181)( 17,182)( 18,173)
( 19,174)( 20,175)( 21,176)( 22,177)( 23,193)( 24,194)( 25,195)( 26,196)
( 27,197)( 28,198)( 29,199)( 30,200)( 31,201)( 32,202)( 33,183)( 34,184)
( 35,185)( 36,186)( 37,187)( 38,188)( 39,189)( 40,190)( 41,191)( 42,192)
( 43,223)( 44,224)( 45,225)( 46,226)( 47,227)( 48,228)( 49,229)( 50,230)
( 51,231)( 52,232)( 53,238)( 54,239)( 55,240)( 56,241)( 57,242)( 58,233)
( 59,234)( 60,235)( 61,236)( 62,237)( 63,203)( 64,204)( 65,205)( 66,206)
( 67,207)( 68,208)( 69,209)( 70,210)( 71,211)( 72,212)( 73,218)( 74,219)
( 75,220)( 76,221)( 77,222)( 78,213)( 79,214)( 80,215)( 81,216)( 82,217)
( 83,243)( 84,244)( 85,245)( 86,246)( 87,247)( 88,248)( 89,249)( 90,250)
( 91,251)( 92,252)( 93,258)( 94,259)( 95,260)( 96,261)( 97,262)( 98,253)
( 99,254)(100,255)(101,256)(102,257)(103,273)(104,274)(105,275)(106,276)
(107,277)(108,278)(109,279)(110,280)(111,281)(112,282)(113,263)(114,264)
(115,265)(116,266)(117,267)(118,268)(119,269)(120,270)(121,271)(122,272)
(123,303)(124,304)(125,305)(126,306)(127,307)(128,308)(129,309)(130,310)
(131,311)(132,312)(133,318)(134,319)(135,320)(136,321)(137,322)(138,313)
(139,314)(140,315)(141,316)(142,317)(143,283)(144,284)(145,285)(146,286)
(147,287)(148,288)(149,289)(150,290)(151,291)(152,292)(153,298)(154,299)
(155,300)(156,301)(157,302)(158,293)(159,294)(160,295)(161,296)(162,297);;
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*s3*s2*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(322)!(1,2);
s1 := Sym(322)!( 3, 83)( 4, 87)( 5, 86)( 6, 85)( 7, 84)( 8, 88)( 9, 92)
( 10, 91)( 11, 90)( 12, 89)( 13, 93)( 14, 97)( 15, 96)( 16, 95)( 17, 94)
( 18, 98)( 19,102)( 20,101)( 21,100)( 22, 99)( 23,103)( 24,107)( 25,106)
( 26,105)( 27,104)( 28,108)( 29,112)( 30,111)( 31,110)( 32,109)( 33,113)
( 34,117)( 35,116)( 36,115)( 37,114)( 38,118)( 39,122)( 40,121)( 41,120)
( 42,119)( 43,123)( 44,127)( 45,126)( 46,125)( 47,124)( 48,128)( 49,132)
( 50,131)( 51,130)( 52,129)( 53,133)( 54,137)( 55,136)( 56,135)( 57,134)
( 58,138)( 59,142)( 60,141)( 61,140)( 62,139)( 63,143)( 64,147)( 65,146)
( 66,145)( 67,144)( 68,148)( 69,152)( 70,151)( 71,150)( 72,149)( 73,153)
( 74,157)( 75,156)( 76,155)( 77,154)( 78,158)( 79,162)( 80,161)( 81,160)
( 82,159)(163,243)(164,247)(165,246)(166,245)(167,244)(168,248)(169,252)
(170,251)(171,250)(172,249)(173,253)(174,257)(175,256)(176,255)(177,254)
(178,258)(179,262)(180,261)(181,260)(182,259)(183,263)(184,267)(185,266)
(186,265)(187,264)(188,268)(189,272)(190,271)(191,270)(192,269)(193,273)
(194,277)(195,276)(196,275)(197,274)(198,278)(199,282)(200,281)(201,280)
(202,279)(203,283)(204,287)(205,286)(206,285)(207,284)(208,288)(209,292)
(210,291)(211,290)(212,289)(213,293)(214,297)(215,296)(216,295)(217,294)
(218,298)(219,302)(220,301)(221,300)(222,299)(223,303)(224,307)(225,306)
(226,305)(227,304)(228,308)(229,312)(230,311)(231,310)(232,309)(233,313)
(234,317)(235,316)(236,315)(237,314)(238,318)(239,322)(240,321)(241,320)
(242,319);
s2 := Sym(322)!( 3, 84)( 4, 83)( 5, 87)( 6, 86)( 7, 85)( 8, 89)( 9, 88)
( 10, 92)( 11, 91)( 12, 90)( 13, 99)( 14, 98)( 15,102)( 16,101)( 17,100)
( 18, 94)( 19, 93)( 20, 97)( 21, 96)( 22, 95)( 23,114)( 24,113)( 25,117)
( 26,116)( 27,115)( 28,119)( 29,118)( 30,122)( 31,121)( 32,120)( 33,104)
( 34,103)( 35,107)( 36,106)( 37,105)( 38,109)( 39,108)( 40,112)( 41,111)
( 42,110)( 43,144)( 44,143)( 45,147)( 46,146)( 47,145)( 48,149)( 49,148)
( 50,152)( 51,151)( 52,150)( 53,159)( 54,158)( 55,162)( 56,161)( 57,160)
( 58,154)( 59,153)( 60,157)( 61,156)( 62,155)( 63,124)( 64,123)( 65,127)
( 66,126)( 67,125)( 68,129)( 69,128)( 70,132)( 71,131)( 72,130)( 73,139)
( 74,138)( 75,142)( 76,141)( 77,140)( 78,134)( 79,133)( 80,137)( 81,136)
( 82,135)(163,284)(164,283)(165,287)(166,286)(167,285)(168,289)(169,288)
(170,292)(171,291)(172,290)(173,299)(174,298)(175,302)(176,301)(177,300)
(178,294)(179,293)(180,297)(181,296)(182,295)(183,314)(184,313)(185,317)
(186,316)(187,315)(188,319)(189,318)(190,322)(191,321)(192,320)(193,304)
(194,303)(195,307)(196,306)(197,305)(198,309)(199,308)(200,312)(201,311)
(202,310)(203,244)(204,243)(205,247)(206,246)(207,245)(208,249)(209,248)
(210,252)(211,251)(212,250)(213,259)(214,258)(215,262)(216,261)(217,260)
(218,254)(219,253)(220,257)(221,256)(222,255)(223,274)(224,273)(225,277)
(226,276)(227,275)(228,279)(229,278)(230,282)(231,281)(232,280)(233,264)
(234,263)(235,267)(236,266)(237,265)(238,269)(239,268)(240,272)(241,271)
(242,270);
s3 := Sym(322)!( 3,163)( 4,164)( 5,165)( 6,166)( 7,167)( 8,168)( 9,169)
( 10,170)( 11,171)( 12,172)( 13,178)( 14,179)( 15,180)( 16,181)( 17,182)
( 18,173)( 19,174)( 20,175)( 21,176)( 22,177)( 23,193)( 24,194)( 25,195)
( 26,196)( 27,197)( 28,198)( 29,199)( 30,200)( 31,201)( 32,202)( 33,183)
( 34,184)( 35,185)( 36,186)( 37,187)( 38,188)( 39,189)( 40,190)( 41,191)
( 42,192)( 43,223)( 44,224)( 45,225)( 46,226)( 47,227)( 48,228)( 49,229)
( 50,230)( 51,231)( 52,232)( 53,238)( 54,239)( 55,240)( 56,241)( 57,242)
( 58,233)( 59,234)( 60,235)( 61,236)( 62,237)( 63,203)( 64,204)( 65,205)
( 66,206)( 67,207)( 68,208)( 69,209)( 70,210)( 71,211)( 72,212)( 73,218)
( 74,219)( 75,220)( 76,221)( 77,222)( 78,213)( 79,214)( 80,215)( 81,216)
( 82,217)( 83,243)( 84,244)( 85,245)( 86,246)( 87,247)( 88,248)( 89,249)
( 90,250)( 91,251)( 92,252)( 93,258)( 94,259)( 95,260)( 96,261)( 97,262)
( 98,253)( 99,254)(100,255)(101,256)(102,257)(103,273)(104,274)(105,275)
(106,276)(107,277)(108,278)(109,279)(110,280)(111,281)(112,282)(113,263)
(114,264)(115,265)(116,266)(117,267)(118,268)(119,269)(120,270)(121,271)
(122,272)(123,303)(124,304)(125,305)(126,306)(127,307)(128,308)(129,309)
(130,310)(131,311)(132,312)(133,318)(134,319)(135,320)(136,321)(137,322)
(138,313)(139,314)(140,315)(141,316)(142,317)(143,283)(144,284)(145,285)
(146,286)(147,287)(148,288)(149,289)(150,290)(151,291)(152,292)(153,298)
(154,299)(155,300)(156,301)(157,302)(158,293)(159,294)(160,295)(161,296)
(162,297);
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*s3*s2*s1*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope