Polytope of Type {44,14}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {44,14}*1232
Also Known As : {44,14|2}. if this polytope has another name.
Group : SmallGroup(1232,98)
Rank : 3
Schlafli Type : {44,14}
Number of vertices, edges, etc : 44, 308, 14
Order of s0s1s2 : 308
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) :
   2-fold quotients : {22,14}*616
   7-fold quotients : {44,2}*176
   11-fold quotients : {4,14}*112
   14-fold quotients : {22,2}*88
   22-fold quotients : {2,14}*56
   28-fold quotients : {11,2}*44
   44-fold quotients : {2,7}*28
   77-fold quotients : {4,2}*16
   154-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 := (  2, 11)(  3, 10)(  4,  9)(  5,  8)(  6,  7)( 13, 22)( 14, 21)( 15, 20)( 16, 19)( 17, 18)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)( 35, 44)( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 46, 55)( 47, 54)( 48, 53)( 49, 52)( 50, 51)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 79, 88)( 80, 87)( 81, 86)( 82, 85)( 83, 84)( 90, 99)( 91, 98)( 92, 97)( 93, 96)( 94, 95)(101,110)(102,109)(103,108)(104,107)(105,106)(112,121)(113,120)(114,119)(115,118)(116,117)(123,132)(124,131)(125,130)(126,129)(127,128)(134,143)(135,142)(136,141)(137,140)(138,139)(145,154)(146,153)(147,152)(148,151)(149,150)(155,232)(156,242)(157,241)(158,240)(159,239)(160,238)(161,237)(162,236)(163,235)(164,234)(165,233)(166,243)(167,253)(168,252)(169,251)(170,250)(171,249)(172,248)(173,247)(174,246)(175,245)(176,244)(177,254)(178,264)(179,263)(180,262)(181,261)(182,260)(183,259)(184,258)(185,257)(186,256)(187,255)(188,265)(189,275)(190,274)(191,273)(192,272)(193,271)(194,270)(195,269)(196,268)(197,267)(198,266)(199,276)(200,286)(201,285)(202,284)(203,283)(204,282)(205,281)(206,280)(207,279)(208,278)(209,277)(210,287)(211,297)(212,296)(213,295)(214,294)(215,293)(216,292)(217,291)(218,290)(219,289)(220,288)(221,298)(222,308)(223,307)(224,306)(225,305)(226,304)(227,303)(228,302)(229,301)(230,300)(231,299);;
s1 := (  1,156)(  2,155)(  3,165)(  4,164)(  5,163)(  6,162)(  7,161)(  8,160)(  9,159)( 10,158)( 11,157)( 12,222)( 13,221)( 14,231)( 15,230)( 16,229)( 17,228)( 18,227)( 19,226)( 20,225)( 21,224)( 22,223)( 23,211)( 24,210)( 25,220)( 26,219)( 27,218)( 28,217)( 29,216)( 30,215)( 31,214)( 32,213)( 33,212)( 34,200)( 35,199)( 36,209)( 37,208)( 38,207)( 39,206)( 40,205)( 41,204)( 42,203)( 43,202)( 44,201)( 45,189)( 46,188)( 47,198)( 48,197)( 49,196)( 50,195)( 51,194)( 52,193)( 53,192)( 54,191)( 55,190)( 56,178)( 57,177)( 58,187)( 59,186)( 60,185)( 61,184)( 62,183)( 63,182)( 64,181)( 65,180)( 66,179)( 67,167)( 68,166)( 69,176)( 70,175)( 71,174)( 72,173)( 73,172)( 74,171)( 75,170)( 76,169)( 77,168)( 78,233)( 79,232)( 80,242)( 81,241)( 82,240)( 83,239)( 84,238)( 85,237)( 86,236)( 87,235)( 88,234)( 89,299)( 90,298)( 91,308)( 92,307)( 93,306)( 94,305)( 95,304)( 96,303)( 97,302)( 98,301)( 99,300)(100,288)(101,287)(102,297)(103,296)(104,295)(105,294)(106,293)(107,292)(108,291)(109,290)(110,289)(111,277)(112,276)(113,286)(114,285)(115,284)(116,283)(117,282)(118,281)(119,280)(120,279)(121,278)(122,266)(123,265)(124,275)(125,274)(126,273)(127,272)(128,271)(129,270)(130,269)(131,268)(132,267)(133,255)(134,254)(135,264)(136,263)(137,262)(138,261)(139,260)(140,259)(141,258)(142,257)(143,256)(144,244)(145,243)(146,253)(147,252)(148,251)(149,250)(150,249)(151,248)(152,247)(153,246)(154,245);;
s2 := (  1, 12)(  2, 13)(  3, 14)(  4, 15)(  5, 16)(  6, 17)(  7, 18)(  8, 19)(  9, 20)( 10, 21)( 11, 22)( 23, 67)( 24, 68)( 25, 69)( 26, 70)( 27, 71)( 28, 72)( 29, 73)( 30, 74)( 31, 75)( 32, 76)( 33, 77)( 34, 56)( 35, 57)( 36, 58)( 37, 59)( 38, 60)( 39, 61)( 40, 62)( 41, 63)( 42, 64)( 43, 65)( 44, 66)( 78, 89)( 79, 90)( 80, 91)( 81, 92)( 82, 93)( 83, 94)( 84, 95)( 85, 96)( 86, 97)( 87, 98)( 88, 99)(100,144)(101,145)(102,146)(103,147)(104,148)(105,149)(106,150)(107,151)(108,152)(109,153)(110,154)(111,133)(112,134)(113,135)(114,136)(115,137)(116,138)(117,139)(118,140)(119,141)(120,142)(121,143)(155,166)(156,167)(157,168)(158,169)(159,170)(160,171)(161,172)(162,173)(163,174)(164,175)(165,176)(177,221)(178,222)(179,223)(180,224)(181,225)(182,226)(183,227)(184,228)(185,229)(186,230)(187,231)(188,210)(189,211)(190,212)(191,213)(192,214)(193,215)(194,216)(195,217)(196,218)(197,219)(198,220)(232,243)(233,244)(234,245)(235,246)(236,247)(237,248)(238,249)(239,250)(240,251)(241,252)(242,253)(254,298)(255,299)(256,300)(257,301)(258,302)(259,303)(260,304)(261,305)(262,306)(263,307)(264,308)(265,287)(266,288)(267,289)(268,290)(269,291)(270,292)(271,293)(272,294)(273,295)(274,296)(275,297);;
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*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*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(308)!(  2, 11)(  3, 10)(  4,  9)(  5,  8)(  6,  7)( 13, 22)( 14, 21)( 15, 20)( 16, 19)( 17, 18)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)( 35, 44)( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 46, 55)( 47, 54)( 48, 53)( 49, 52)( 50, 51)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 79, 88)( 80, 87)( 81, 86)( 82, 85)( 83, 84)( 90, 99)( 91, 98)( 92, 97)( 93, 96)( 94, 95)(101,110)(102,109)(103,108)(104,107)(105,106)(112,121)(113,120)(114,119)(115,118)(116,117)(123,132)(124,131)(125,130)(126,129)(127,128)(134,143)(135,142)(136,141)(137,140)(138,139)(145,154)(146,153)(147,152)(148,151)(149,150)(155,232)(156,242)(157,241)(158,240)(159,239)(160,238)(161,237)(162,236)(163,235)(164,234)(165,233)(166,243)(167,253)(168,252)(169,251)(170,250)(171,249)(172,248)(173,247)(174,246)(175,245)(176,244)(177,254)(178,264)(179,263)(180,262)(181,261)(182,260)(183,259)(184,258)(185,257)(186,256)(187,255)(188,265)(189,275)(190,274)(191,273)(192,272)(193,271)(194,270)(195,269)(196,268)(197,267)(198,266)(199,276)(200,286)(201,285)(202,284)(203,283)(204,282)(205,281)(206,280)(207,279)(208,278)(209,277)(210,287)(211,297)(212,296)(213,295)(214,294)(215,293)(216,292)(217,291)(218,290)(219,289)(220,288)(221,298)(222,308)(223,307)(224,306)(225,305)(226,304)(227,303)(228,302)(229,301)(230,300)(231,299);
s1 := Sym(308)!(  1,156)(  2,155)(  3,165)(  4,164)(  5,163)(  6,162)(  7,161)(  8,160)(  9,159)( 10,158)( 11,157)( 12,222)( 13,221)( 14,231)( 15,230)( 16,229)( 17,228)( 18,227)( 19,226)( 20,225)( 21,224)( 22,223)( 23,211)( 24,210)( 25,220)( 26,219)( 27,218)( 28,217)( 29,216)( 30,215)( 31,214)( 32,213)( 33,212)( 34,200)( 35,199)( 36,209)( 37,208)( 38,207)( 39,206)( 40,205)( 41,204)( 42,203)( 43,202)( 44,201)( 45,189)( 46,188)( 47,198)( 48,197)( 49,196)( 50,195)( 51,194)( 52,193)( 53,192)( 54,191)( 55,190)( 56,178)( 57,177)( 58,187)( 59,186)( 60,185)( 61,184)( 62,183)( 63,182)( 64,181)( 65,180)( 66,179)( 67,167)( 68,166)( 69,176)( 70,175)( 71,174)( 72,173)( 73,172)( 74,171)( 75,170)( 76,169)( 77,168)( 78,233)( 79,232)( 80,242)( 81,241)( 82,240)( 83,239)( 84,238)( 85,237)( 86,236)( 87,235)( 88,234)( 89,299)( 90,298)( 91,308)( 92,307)( 93,306)( 94,305)( 95,304)( 96,303)( 97,302)( 98,301)( 99,300)(100,288)(101,287)(102,297)(103,296)(104,295)(105,294)(106,293)(107,292)(108,291)(109,290)(110,289)(111,277)(112,276)(113,286)(114,285)(115,284)(116,283)(117,282)(118,281)(119,280)(120,279)(121,278)(122,266)(123,265)(124,275)(125,274)(126,273)(127,272)(128,271)(129,270)(130,269)(131,268)(132,267)(133,255)(134,254)(135,264)(136,263)(137,262)(138,261)(139,260)(140,259)(141,258)(142,257)(143,256)(144,244)(145,243)(146,253)(147,252)(148,251)(149,250)(150,249)(151,248)(152,247)(153,246)(154,245);
s2 := Sym(308)!(  1, 12)(  2, 13)(  3, 14)(  4, 15)(  5, 16)(  6, 17)(  7, 18)(  8, 19)(  9, 20)( 10, 21)( 11, 22)( 23, 67)( 24, 68)( 25, 69)( 26, 70)( 27, 71)( 28, 72)( 29, 73)( 30, 74)( 31, 75)( 32, 76)( 33, 77)( 34, 56)( 35, 57)( 36, 58)( 37, 59)( 38, 60)( 39, 61)( 40, 62)( 41, 63)( 42, 64)( 43, 65)( 44, 66)( 78, 89)( 79, 90)( 80, 91)( 81, 92)( 82, 93)( 83, 94)( 84, 95)( 85, 96)( 86, 97)( 87, 98)( 88, 99)(100,144)(101,145)(102,146)(103,147)(104,148)(105,149)(106,150)(107,151)(108,152)(109,153)(110,154)(111,133)(112,134)(113,135)(114,136)(115,137)(116,138)(117,139)(118,140)(119,141)(120,142)(121,143)(155,166)(156,167)(157,168)(158,169)(159,170)(160,171)(161,172)(162,173)(163,174)(164,175)(165,176)(177,221)(178,222)(179,223)(180,224)(181,225)(182,226)(183,227)(184,228)(185,229)(186,230)(187,231)(188,210)(189,211)(190,212)(191,213)(192,214)(193,215)(194,216)(195,217)(196,218)(197,219)(198,220)(232,243)(233,244)(234,245)(235,246)(236,247)(237,248)(238,249)(239,250)(240,251)(241,252)(242,253)(254,298)(255,299)(256,300)(257,301)(258,302)(259,303)(260,304)(261,305)(262,306)(263,307)(264,308)(265,287)(266,288)(267,289)(268,290)(269,291)(270,292)(271,293)(272,294)(273,295)(274,296)(275,297);
poly := sub<Sym(308)|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*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*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

Twisty Puzzle