Polytope of Type {10,10,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,10,2}*1280d
if this polytope has a name.
Group : SmallGroup(1280,1116461)
Rank : 4
Schlafli Type : {10,10,2}
Number of vertices, edges, etc : 32, 160, 32, 2
Order of s0s1s2s3 : 4
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 : {5,10,2}*640b, {10,5,2}*640b
4-fold quotients : {5,5,2}*320
80-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 11)( 3, 14)( 4, 8)( 6, 15)( 7, 10)( 9, 13)( 17, 65)( 18, 75)
( 19, 78)( 20, 72)( 21, 69)( 22, 79)( 23, 74)( 24, 68)( 25, 77)( 26, 71)
( 27, 66)( 28, 76)( 29, 73)( 30, 67)( 31, 70)( 32, 80)( 33, 49)( 34, 59)
( 35, 62)( 36, 56)( 37, 53)( 38, 63)( 39, 58)( 40, 52)( 41, 61)( 42, 55)
( 43, 50)( 44, 60)( 45, 57)( 46, 51)( 47, 54)( 48, 64)( 82, 91)( 83, 94)
( 84, 88)( 86, 95)( 87, 90)( 89, 93)( 97,145)( 98,155)( 99,158)(100,152)
(101,149)(102,159)(103,154)(104,148)(105,157)(106,151)(107,146)(108,156)
(109,153)(110,147)(111,150)(112,160)(113,129)(114,139)(115,142)(116,136)
(117,133)(118,143)(119,138)(120,132)(121,141)(122,135)(123,130)(124,140)
(125,137)(126,131)(127,134)(128,144)(162,171)(163,174)(164,168)(166,175)
(167,170)(169,173)(177,225)(178,235)(179,238)(180,232)(181,229)(182,239)
(183,234)(184,228)(185,237)(186,231)(187,226)(188,236)(189,233)(190,227)
(191,230)(192,240)(193,209)(194,219)(195,222)(196,216)(197,213)(198,223)
(199,218)(200,212)(201,221)(202,215)(203,210)(204,220)(205,217)(206,211)
(207,214)(208,224)(242,251)(243,254)(244,248)(246,255)(247,250)(249,253)
(257,305)(258,315)(259,318)(260,312)(261,309)(262,319)(263,314)(264,308)
(265,317)(266,311)(267,306)(268,316)(269,313)(270,307)(271,310)(272,320)
(273,289)(274,299)(275,302)(276,296)(277,293)(278,303)(279,298)(280,292)
(281,301)(282,295)(283,290)(284,300)(285,297)(286,291)(287,294)(288,304);;
s1 := ( 1,177)( 2,192)( 3,179)( 4,190)( 5,183)( 6,186)( 7,181)( 8,188)
( 9,187)( 10,182)( 11,185)( 12,184)( 13,189)( 14,180)( 15,191)( 16,178)
( 17,161)( 18,176)( 19,163)( 20,174)( 21,167)( 22,170)( 23,165)( 24,172)
( 25,171)( 26,166)( 27,169)( 28,168)( 29,173)( 30,164)( 31,175)( 32,162)
( 33,225)( 34,240)( 35,227)( 36,238)( 37,231)( 38,234)( 39,229)( 40,236)
( 41,235)( 42,230)( 43,233)( 44,232)( 45,237)( 46,228)( 47,239)( 48,226)
( 49,209)( 50,224)( 51,211)( 52,222)( 53,215)( 54,218)( 55,213)( 56,220)
( 57,219)( 58,214)( 59,217)( 60,216)( 61,221)( 62,212)( 63,223)( 64,210)
( 65,193)( 66,208)( 67,195)( 68,206)( 69,199)( 70,202)( 71,197)( 72,204)
( 73,203)( 74,198)( 75,201)( 76,200)( 77,205)( 78,196)( 79,207)( 80,194)
( 81,257)( 82,272)( 83,259)( 84,270)( 85,263)( 86,266)( 87,261)( 88,268)
( 89,267)( 90,262)( 91,265)( 92,264)( 93,269)( 94,260)( 95,271)( 96,258)
( 97,241)( 98,256)( 99,243)(100,254)(101,247)(102,250)(103,245)(104,252)
(105,251)(106,246)(107,249)(108,248)(109,253)(110,244)(111,255)(112,242)
(113,305)(114,320)(115,307)(116,318)(117,311)(118,314)(119,309)(120,316)
(121,315)(122,310)(123,313)(124,312)(125,317)(126,308)(127,319)(128,306)
(129,289)(130,304)(131,291)(132,302)(133,295)(134,298)(135,293)(136,300)
(137,299)(138,294)(139,297)(140,296)(141,301)(142,292)(143,303)(144,290)
(145,273)(146,288)(147,275)(148,286)(149,279)(150,282)(151,277)(152,284)
(153,283)(154,278)(155,281)(156,280)(157,285)(158,276)(159,287)(160,274);;
s2 := ( 1, 85)( 2, 95)( 3, 90)( 4, 84)( 5, 81)( 6, 91)( 7, 94)( 8, 88)
( 9, 89)( 10, 83)( 11, 86)( 12, 96)( 13, 93)( 14, 87)( 15, 82)( 16, 92)
( 17,149)( 18,159)( 19,154)( 20,148)( 21,145)( 22,155)( 23,158)( 24,152)
( 25,153)( 26,147)( 27,150)( 28,160)( 29,157)( 30,151)( 31,146)( 32,156)
( 33,133)( 34,143)( 35,138)( 36,132)( 37,129)( 38,139)( 39,142)( 40,136)
( 41,137)( 42,131)( 43,134)( 44,144)( 45,141)( 46,135)( 47,130)( 48,140)
( 49,117)( 50,127)( 51,122)( 52,116)( 53,113)( 54,123)( 55,126)( 56,120)
( 57,121)( 58,115)( 59,118)( 60,128)( 61,125)( 62,119)( 63,114)( 64,124)
( 65,101)( 66,111)( 67,106)( 68,100)( 69, 97)( 70,107)( 71,110)( 72,104)
( 73,105)( 74, 99)( 75,102)( 76,112)( 77,109)( 78,103)( 79, 98)( 80,108)
(161,245)(162,255)(163,250)(164,244)(165,241)(166,251)(167,254)(168,248)
(169,249)(170,243)(171,246)(172,256)(173,253)(174,247)(175,242)(176,252)
(177,309)(178,319)(179,314)(180,308)(181,305)(182,315)(183,318)(184,312)
(185,313)(186,307)(187,310)(188,320)(189,317)(190,311)(191,306)(192,316)
(193,293)(194,303)(195,298)(196,292)(197,289)(198,299)(199,302)(200,296)
(201,297)(202,291)(203,294)(204,304)(205,301)(206,295)(207,290)(208,300)
(209,277)(210,287)(211,282)(212,276)(213,273)(214,283)(215,286)(216,280)
(217,281)(218,275)(219,278)(220,288)(221,285)(222,279)(223,274)(224,284)
(225,261)(226,271)(227,266)(228,260)(229,257)(230,267)(231,270)(232,264)
(233,265)(234,259)(235,262)(236,272)(237,269)(238,263)(239,258)(240,268);;
s3 := (321,322);;
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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*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*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(322)!( 2, 11)( 3, 14)( 4, 8)( 6, 15)( 7, 10)( 9, 13)( 17, 65)
( 18, 75)( 19, 78)( 20, 72)( 21, 69)( 22, 79)( 23, 74)( 24, 68)( 25, 77)
( 26, 71)( 27, 66)( 28, 76)( 29, 73)( 30, 67)( 31, 70)( 32, 80)( 33, 49)
( 34, 59)( 35, 62)( 36, 56)( 37, 53)( 38, 63)( 39, 58)( 40, 52)( 41, 61)
( 42, 55)( 43, 50)( 44, 60)( 45, 57)( 46, 51)( 47, 54)( 48, 64)( 82, 91)
( 83, 94)( 84, 88)( 86, 95)( 87, 90)( 89, 93)( 97,145)( 98,155)( 99,158)
(100,152)(101,149)(102,159)(103,154)(104,148)(105,157)(106,151)(107,146)
(108,156)(109,153)(110,147)(111,150)(112,160)(113,129)(114,139)(115,142)
(116,136)(117,133)(118,143)(119,138)(120,132)(121,141)(122,135)(123,130)
(124,140)(125,137)(126,131)(127,134)(128,144)(162,171)(163,174)(164,168)
(166,175)(167,170)(169,173)(177,225)(178,235)(179,238)(180,232)(181,229)
(182,239)(183,234)(184,228)(185,237)(186,231)(187,226)(188,236)(189,233)
(190,227)(191,230)(192,240)(193,209)(194,219)(195,222)(196,216)(197,213)
(198,223)(199,218)(200,212)(201,221)(202,215)(203,210)(204,220)(205,217)
(206,211)(207,214)(208,224)(242,251)(243,254)(244,248)(246,255)(247,250)
(249,253)(257,305)(258,315)(259,318)(260,312)(261,309)(262,319)(263,314)
(264,308)(265,317)(266,311)(267,306)(268,316)(269,313)(270,307)(271,310)
(272,320)(273,289)(274,299)(275,302)(276,296)(277,293)(278,303)(279,298)
(280,292)(281,301)(282,295)(283,290)(284,300)(285,297)(286,291)(287,294)
(288,304);
s1 := Sym(322)!( 1,177)( 2,192)( 3,179)( 4,190)( 5,183)( 6,186)( 7,181)
( 8,188)( 9,187)( 10,182)( 11,185)( 12,184)( 13,189)( 14,180)( 15,191)
( 16,178)( 17,161)( 18,176)( 19,163)( 20,174)( 21,167)( 22,170)( 23,165)
( 24,172)( 25,171)( 26,166)( 27,169)( 28,168)( 29,173)( 30,164)( 31,175)
( 32,162)( 33,225)( 34,240)( 35,227)( 36,238)( 37,231)( 38,234)( 39,229)
( 40,236)( 41,235)( 42,230)( 43,233)( 44,232)( 45,237)( 46,228)( 47,239)
( 48,226)( 49,209)( 50,224)( 51,211)( 52,222)( 53,215)( 54,218)( 55,213)
( 56,220)( 57,219)( 58,214)( 59,217)( 60,216)( 61,221)( 62,212)( 63,223)
( 64,210)( 65,193)( 66,208)( 67,195)( 68,206)( 69,199)( 70,202)( 71,197)
( 72,204)( 73,203)( 74,198)( 75,201)( 76,200)( 77,205)( 78,196)( 79,207)
( 80,194)( 81,257)( 82,272)( 83,259)( 84,270)( 85,263)( 86,266)( 87,261)
( 88,268)( 89,267)( 90,262)( 91,265)( 92,264)( 93,269)( 94,260)( 95,271)
( 96,258)( 97,241)( 98,256)( 99,243)(100,254)(101,247)(102,250)(103,245)
(104,252)(105,251)(106,246)(107,249)(108,248)(109,253)(110,244)(111,255)
(112,242)(113,305)(114,320)(115,307)(116,318)(117,311)(118,314)(119,309)
(120,316)(121,315)(122,310)(123,313)(124,312)(125,317)(126,308)(127,319)
(128,306)(129,289)(130,304)(131,291)(132,302)(133,295)(134,298)(135,293)
(136,300)(137,299)(138,294)(139,297)(140,296)(141,301)(142,292)(143,303)
(144,290)(145,273)(146,288)(147,275)(148,286)(149,279)(150,282)(151,277)
(152,284)(153,283)(154,278)(155,281)(156,280)(157,285)(158,276)(159,287)
(160,274);
s2 := Sym(322)!( 1, 85)( 2, 95)( 3, 90)( 4, 84)( 5, 81)( 6, 91)( 7, 94)
( 8, 88)( 9, 89)( 10, 83)( 11, 86)( 12, 96)( 13, 93)( 14, 87)( 15, 82)
( 16, 92)( 17,149)( 18,159)( 19,154)( 20,148)( 21,145)( 22,155)( 23,158)
( 24,152)( 25,153)( 26,147)( 27,150)( 28,160)( 29,157)( 30,151)( 31,146)
( 32,156)( 33,133)( 34,143)( 35,138)( 36,132)( 37,129)( 38,139)( 39,142)
( 40,136)( 41,137)( 42,131)( 43,134)( 44,144)( 45,141)( 46,135)( 47,130)
( 48,140)( 49,117)( 50,127)( 51,122)( 52,116)( 53,113)( 54,123)( 55,126)
( 56,120)( 57,121)( 58,115)( 59,118)( 60,128)( 61,125)( 62,119)( 63,114)
( 64,124)( 65,101)( 66,111)( 67,106)( 68,100)( 69, 97)( 70,107)( 71,110)
( 72,104)( 73,105)( 74, 99)( 75,102)( 76,112)( 77,109)( 78,103)( 79, 98)
( 80,108)(161,245)(162,255)(163,250)(164,244)(165,241)(166,251)(167,254)
(168,248)(169,249)(170,243)(171,246)(172,256)(173,253)(174,247)(175,242)
(176,252)(177,309)(178,319)(179,314)(180,308)(181,305)(182,315)(183,318)
(184,312)(185,313)(186,307)(187,310)(188,320)(189,317)(190,311)(191,306)
(192,316)(193,293)(194,303)(195,298)(196,292)(197,289)(198,299)(199,302)
(200,296)(201,297)(202,291)(203,294)(204,304)(205,301)(206,295)(207,290)
(208,300)(209,277)(210,287)(211,282)(212,276)(213,273)(214,283)(215,286)
(216,280)(217,281)(218,275)(219,278)(220,288)(221,285)(222,279)(223,274)
(224,284)(225,261)(226,271)(227,266)(228,260)(229,257)(230,267)(231,270)
(232,264)(233,265)(234,259)(235,262)(236,272)(237,269)(238,263)(239,258)
(240,268);
s3 := Sym(322)!(321,322);
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*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*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1 >;
to this polytope