Polytope of Type {10,70}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,70}*1400b
Also Known As : {10,70|2}. if this polytope has another name.
Group : SmallGroup(1400,146)
Rank : 3
Schlafli Type : {10,70}
Number of vertices, edges, etc : 10, 350, 70
Order of s0s1s2 : 70
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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) :
   5-fold quotients : {10,14}*280, {2,70}*280
   7-fold quotients : {10,10}*200a
   10-fold quotients : {2,35}*140
   25-fold quotients : {2,14}*56
   35-fold quotients : {2,10}*40, {10,2}*40
   50-fold quotients : {2,7}*28
   70-fold quotients : {2,5}*20, {5,2}*20
   175-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   None.

Permutation Representation (GAP) : 
s0 := ( 36,141)( 37,142)( 38,143)( 39,144)( 40,145)( 41,146)( 42,147)( 43,148)( 44,149)( 45,150)( 46,151)( 47,152)( 48,153)( 49,154)( 50,155)( 51,156)( 52,157)( 53,158)( 54,159)( 55,160)( 56,161)( 57,162)( 58,163)( 59,164)( 60,165)( 61,166)( 62,167)( 63,168)( 64,169)( 65,170)( 66,171)( 67,172)( 68,173)( 69,174)( 70,175)( 71,106)( 72,107)( 73,108)( 74,109)( 75,110)( 76,111)( 77,112)( 78,113)( 79,114)( 80,115)( 81,116)( 82,117)( 83,118)( 84,119)( 85,120)( 86,121)( 87,122)( 88,123)( 89,124)( 90,125)( 91,126)( 92,127)( 93,128)( 94,129)( 95,130)( 96,131)( 97,132)( 98,133)( 99,134)(100,135)(101,136)(102,137)(103,138)(104,139)(105,140)(211,316)(212,317)(213,318)(214,319)(215,320)(216,321)(217,322)(218,323)(219,324)(220,325)(221,326)(222,327)(223,328)(224,329)(225,330)(226,331)(227,332)(228,333)(229,334)(230,335)(231,336)(232,337)(233,338)(234,339)(235,340)(236,341)(237,342)(238,343)(239,344)(240,345)(241,346)(242,347)(243,348)(244,349)(245,350)(246,281)(247,282)(248,283)(249,284)(250,285)(251,286)(252,287)(253,288)(254,289)(255,290)(256,291)(257,292)(258,293)(259,294)(260,295)(261,296)(262,297)(263,298)(264,299)(265,300)(266,301)(267,302)(268,303)(269,304)(270,305)(271,306)(272,307)(273,308)(274,309)(275,310)(276,311)(277,312)(278,313)(279,314)(280,315);;
s1 := (  1, 36)(  2, 42)(  3, 41)(  4, 40)(  5, 39)(  6, 38)(  7, 37)(  8, 64)(  9, 70)( 10, 69)( 11, 68)( 12, 67)( 13, 66)( 14, 65)( 15, 57)( 16, 63)( 17, 62)( 18, 61)( 19, 60)( 20, 59)( 21, 58)( 22, 50)( 23, 56)( 24, 55)( 25, 54)( 26, 53)( 27, 52)( 28, 51)( 29, 43)( 30, 49)( 31, 48)( 32, 47)( 33, 46)( 34, 45)( 35, 44)( 71,141)( 72,147)( 73,146)( 74,145)( 75,144)( 76,143)( 77,142)( 78,169)( 79,175)( 80,174)( 81,173)( 82,172)( 83,171)( 84,170)( 85,162)( 86,168)( 87,167)( 88,166)( 89,165)( 90,164)( 91,163)( 92,155)( 93,161)( 94,160)( 95,159)( 96,158)( 97,157)( 98,156)( 99,148)(100,154)(101,153)(102,152)(103,151)(104,150)(105,149)(107,112)(108,111)(109,110)(113,134)(114,140)(115,139)(116,138)(117,137)(118,136)(119,135)(120,127)(121,133)(122,132)(123,131)(124,130)(125,129)(126,128)(176,211)(177,217)(178,216)(179,215)(180,214)(181,213)(182,212)(183,239)(184,245)(185,244)(186,243)(187,242)(188,241)(189,240)(190,232)(191,238)(192,237)(193,236)(194,235)(195,234)(196,233)(197,225)(198,231)(199,230)(200,229)(201,228)(202,227)(203,226)(204,218)(205,224)(206,223)(207,222)(208,221)(209,220)(210,219)(246,316)(247,322)(248,321)(249,320)(250,319)(251,318)(252,317)(253,344)(254,350)(255,349)(256,348)(257,347)(258,346)(259,345)(260,337)(261,343)(262,342)(263,341)(264,340)(265,339)(266,338)(267,330)(268,336)(269,335)(270,334)(271,333)(272,332)(273,331)(274,323)(275,329)(276,328)(277,327)(278,326)(279,325)(280,324)(282,287)(283,286)(284,285)(288,309)(289,315)(290,314)(291,313)(292,312)(293,311)(294,310)(295,302)(296,308)(297,307)(298,306)(299,305)(300,304)(301,303);;
s2 := (  1,184)(  2,183)(  3,189)(  4,188)(  5,187)(  6,186)(  7,185)(  8,177)(  9,176)( 10,182)( 11,181)( 12,180)( 13,179)( 14,178)( 15,205)( 16,204)( 17,210)( 18,209)( 19,208)( 20,207)( 21,206)( 22,198)( 23,197)( 24,203)( 25,202)( 26,201)( 27,200)( 28,199)( 29,191)( 30,190)( 31,196)( 32,195)( 33,194)( 34,193)( 35,192)( 36,219)( 37,218)( 38,224)( 39,223)( 40,222)( 41,221)( 42,220)( 43,212)( 44,211)( 45,217)( 46,216)( 47,215)( 48,214)( 49,213)( 50,240)( 51,239)( 52,245)( 53,244)( 54,243)( 55,242)( 56,241)( 57,233)( 58,232)( 59,238)( 60,237)( 61,236)( 62,235)( 63,234)( 64,226)( 65,225)( 66,231)( 67,230)( 68,229)( 69,228)( 70,227)( 71,254)( 72,253)( 73,259)( 74,258)( 75,257)( 76,256)( 77,255)( 78,247)( 79,246)( 80,252)( 81,251)( 82,250)( 83,249)( 84,248)( 85,275)( 86,274)( 87,280)( 88,279)( 89,278)( 90,277)( 91,276)( 92,268)( 93,267)( 94,273)( 95,272)( 96,271)( 97,270)( 98,269)( 99,261)(100,260)(101,266)(102,265)(103,264)(104,263)(105,262)(106,289)(107,288)(108,294)(109,293)(110,292)(111,291)(112,290)(113,282)(114,281)(115,287)(116,286)(117,285)(118,284)(119,283)(120,310)(121,309)(122,315)(123,314)(124,313)(125,312)(126,311)(127,303)(128,302)(129,308)(130,307)(131,306)(132,305)(133,304)(134,296)(135,295)(136,301)(137,300)(138,299)(139,298)(140,297)(141,324)(142,323)(143,329)(144,328)(145,327)(146,326)(147,325)(148,317)(149,316)(150,322)(151,321)(152,320)(153,319)(154,318)(155,345)(156,344)(157,350)(158,349)(159,348)(160,347)(161,346)(162,338)(163,337)(164,343)(165,342)(166,341)(167,340)(168,339)(169,331)(170,330)(171,336)(172,335)(173,334)(174,333)(175,332);;
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*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(350)!( 36,141)( 37,142)( 38,143)( 39,144)( 40,145)( 41,146)( 42,147)( 43,148)( 44,149)( 45,150)( 46,151)( 47,152)( 48,153)( 49,154)( 50,155)( 51,156)( 52,157)( 53,158)( 54,159)( 55,160)( 56,161)( 57,162)( 58,163)( 59,164)( 60,165)( 61,166)( 62,167)( 63,168)( 64,169)( 65,170)( 66,171)( 67,172)( 68,173)( 69,174)( 70,175)( 71,106)( 72,107)( 73,108)( 74,109)( 75,110)( 76,111)( 77,112)( 78,113)( 79,114)( 80,115)( 81,116)( 82,117)( 83,118)( 84,119)( 85,120)( 86,121)( 87,122)( 88,123)( 89,124)( 90,125)( 91,126)( 92,127)( 93,128)( 94,129)( 95,130)( 96,131)( 97,132)( 98,133)( 99,134)(100,135)(101,136)(102,137)(103,138)(104,139)(105,140)(211,316)(212,317)(213,318)(214,319)(215,320)(216,321)(217,322)(218,323)(219,324)(220,325)(221,326)(222,327)(223,328)(224,329)(225,330)(226,331)(227,332)(228,333)(229,334)(230,335)(231,336)(232,337)(233,338)(234,339)(235,340)(236,341)(237,342)(238,343)(239,344)(240,345)(241,346)(242,347)(243,348)(244,349)(245,350)(246,281)(247,282)(248,283)(249,284)(250,285)(251,286)(252,287)(253,288)(254,289)(255,290)(256,291)(257,292)(258,293)(259,294)(260,295)(261,296)(262,297)(263,298)(264,299)(265,300)(266,301)(267,302)(268,303)(269,304)(270,305)(271,306)(272,307)(273,308)(274,309)(275,310)(276,311)(277,312)(278,313)(279,314)(280,315);
s1 := Sym(350)!(  1, 36)(  2, 42)(  3, 41)(  4, 40)(  5, 39)(  6, 38)(  7, 37)(  8, 64)(  9, 70)( 10, 69)( 11, 68)( 12, 67)( 13, 66)( 14, 65)( 15, 57)( 16, 63)( 17, 62)( 18, 61)( 19, 60)( 20, 59)( 21, 58)( 22, 50)( 23, 56)( 24, 55)( 25, 54)( 26, 53)( 27, 52)( 28, 51)( 29, 43)( 30, 49)( 31, 48)( 32, 47)( 33, 46)( 34, 45)( 35, 44)( 71,141)( 72,147)( 73,146)( 74,145)( 75,144)( 76,143)( 77,142)( 78,169)( 79,175)( 80,174)( 81,173)( 82,172)( 83,171)( 84,170)( 85,162)( 86,168)( 87,167)( 88,166)( 89,165)( 90,164)( 91,163)( 92,155)( 93,161)( 94,160)( 95,159)( 96,158)( 97,157)( 98,156)( 99,148)(100,154)(101,153)(102,152)(103,151)(104,150)(105,149)(107,112)(108,111)(109,110)(113,134)(114,140)(115,139)(116,138)(117,137)(118,136)(119,135)(120,127)(121,133)(122,132)(123,131)(124,130)(125,129)(126,128)(176,211)(177,217)(178,216)(179,215)(180,214)(181,213)(182,212)(183,239)(184,245)(185,244)(186,243)(187,242)(188,241)(189,240)(190,232)(191,238)(192,237)(193,236)(194,235)(195,234)(196,233)(197,225)(198,231)(199,230)(200,229)(201,228)(202,227)(203,226)(204,218)(205,224)(206,223)(207,222)(208,221)(209,220)(210,219)(246,316)(247,322)(248,321)(249,320)(250,319)(251,318)(252,317)(253,344)(254,350)(255,349)(256,348)(257,347)(258,346)(259,345)(260,337)(261,343)(262,342)(263,341)(264,340)(265,339)(266,338)(267,330)(268,336)(269,335)(270,334)(271,333)(272,332)(273,331)(274,323)(275,329)(276,328)(277,327)(278,326)(279,325)(280,324)(282,287)(283,286)(284,285)(288,309)(289,315)(290,314)(291,313)(292,312)(293,311)(294,310)(295,302)(296,308)(297,307)(298,306)(299,305)(300,304)(301,303);
s2 := Sym(350)!(  1,184)(  2,183)(  3,189)(  4,188)(  5,187)(  6,186)(  7,185)(  8,177)(  9,176)( 10,182)( 11,181)( 12,180)( 13,179)( 14,178)( 15,205)( 16,204)( 17,210)( 18,209)( 19,208)( 20,207)( 21,206)( 22,198)( 23,197)( 24,203)( 25,202)( 26,201)( 27,200)( 28,199)( 29,191)( 30,190)( 31,196)( 32,195)( 33,194)( 34,193)( 35,192)( 36,219)( 37,218)( 38,224)( 39,223)( 40,222)( 41,221)( 42,220)( 43,212)( 44,211)( 45,217)( 46,216)( 47,215)( 48,214)( 49,213)( 50,240)( 51,239)( 52,245)( 53,244)( 54,243)( 55,242)( 56,241)( 57,233)( 58,232)( 59,238)( 60,237)( 61,236)( 62,235)( 63,234)( 64,226)( 65,225)( 66,231)( 67,230)( 68,229)( 69,228)( 70,227)( 71,254)( 72,253)( 73,259)( 74,258)( 75,257)( 76,256)( 77,255)( 78,247)( 79,246)( 80,252)( 81,251)( 82,250)( 83,249)( 84,248)( 85,275)( 86,274)( 87,280)( 88,279)( 89,278)( 90,277)( 91,276)( 92,268)( 93,267)( 94,273)( 95,272)( 96,271)( 97,270)( 98,269)( 99,261)(100,260)(101,266)(102,265)(103,264)(104,263)(105,262)(106,289)(107,288)(108,294)(109,293)(110,292)(111,291)(112,290)(113,282)(114,281)(115,287)(116,286)(117,285)(118,284)(119,283)(120,310)(121,309)(122,315)(123,314)(124,313)(125,312)(126,311)(127,303)(128,302)(129,308)(130,307)(131,306)(132,305)(133,304)(134,296)(135,295)(136,301)(137,300)(138,299)(139,298)(140,297)(141,324)(142,323)(143,329)(144,328)(145,327)(146,326)(147,325)(148,317)(149,316)(150,322)(151,321)(152,320)(153,319)(154,318)(155,345)(156,344)(157,350)(158,349)(159,348)(160,347)(161,346)(162,338)(163,337)(164,343)(165,342)(166,341)(167,340)(168,339)(169,331)(170,330)(171,336)(172,335)(173,334)(174,333)(175,332);
poly := sub<Sym(350)|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*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope

Twisty Puzzle