Polytope of Type {6,14}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,14}*1176b
if this polytope has a name.
Group : SmallGroup(1176,225)
Rank : 3
Schlafli Type : {6,14}
Number of vertices, edges, etc : 42, 294, 98
Order of s₀s₁s₂ : 6
Order of s₀s₁s₂s₁ : 14
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,14}*588
   49-fold quotients : {6,2}*24
   98-fold quotients : {3,2}*12
   147-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2> of order 7.
      14 facets:
         14 of {6}*12
      6 vertex figures:
         6 of {14}*28
   P/N, where N=<s1*s2*s1*s2> of order 7.
      14 facets:
         14 of {6}*12
      18 vertex figures:
         14 of {2}*4
         4 of {14}*28
   P/N, where N=<s0*s1*s0*s2*s1*s2*s1*s0*s2*s1*s0*s2> of order 7.
      14 facets:
         14 of {6}*12
      6 vertex figures:
         6 of {14}*28

Permutation Representation (GAP) :

s0 := (  2, 46)(  3, 42)(  4, 31)(  5, 27)(  6, 16)(  7, 12)(  8, 30)(  9, 26)( 10, 15)( 13, 45)( 14, 41)( 17, 44)( 18, 40)( 19, 29)( 20, 25)( 22, 39)( 23, 35)( 28, 43)( 32, 49)( 33, 38)( 36, 48)( 50, 99)( 51,144)( 52,140)( 53,129)( 54,125)( 55,114)( 56,110)( 57,128)( 58,124)( 59,113)( 60,109)( 61,105)( 62,143)( 63,139)( 64,108)( 65,104)( 66,142)( 67,138)( 68,127)( 69,123)( 70,119)( 71,137)( 72,133)( 73,122)( 74,118)( 75,107)( 76,103)( 77,141)( 78,117)( 79,106)( 80,102)( 81,147)( 82,136)( 83,132)( 84,121)( 85,146)( 86,135)( 87,131)( 88,120)( 89,116)( 90,112)( 91,101)( 92,126)( 93,115)( 94,111)( 95,100)( 96,145)( 97,134)( 98,130)(149,193)(150,189)(151,178)(152,174)(153,163)(154,159)(155,177)(156,173)(157,162)(160,192)(161,188)(164,191)(165,187)(166,176)(167,172)(169,186)(170,182)(175,190)(179,196)(180,185)(183,195)(197,246)(198,291)(199,287)(200,276)(201,272)(202,261)(203,257)(204,275)(205,271)(206,260)(207,256)(208,252)(209,290)(210,286)(211,255)(212,251)(213,289)(214,285)(215,274)(216,270)(217,266)(218,284)(219,280)(220,269)(221,265)(222,254)(223,250)(224,288)(225,264)(226,253)(227,249)(228,294)(229,283)(230,279)(231,268)(232,293)(233,282)(234,278)(235,267)(236,263)(237,259)(238,248)(239,273)(240,262)(241,258)(242,247)(243,292)(244,281)(245,277);;
s1 := (  1,197)(  2,238)(  3,223)(  4,208)(  5,242)(  6,227)(  7,212)(  8,204)(  9,245)( 10,230)( 11,215)( 12,200)( 13,234)( 14,219)( 15,211)( 16,203)( 17,237)( 18,222)( 19,207)( 20,241)( 21,226)( 22,218)( 23,210)( 24,244)( 25,229)( 26,214)( 27,199)( 28,233)( 29,225)( 30,217)( 31,202)( 32,236)( 33,221)( 34,206)( 35,240)( 36,232)( 37,224)( 38,209)( 39,243)( 40,228)( 41,213)( 42,198)( 43,239)( 44,231)( 45,216)( 46,201)( 47,235)( 48,220)( 49,205)( 50,148)( 51,189)( 52,174)( 53,159)( 54,193)( 55,178)( 56,163)( 57,155)( 58,196)( 59,181)( 60,166)( 61,151)( 62,185)( 63,170)( 64,162)( 65,154)( 66,188)( 67,173)( 68,158)( 69,192)( 70,177)( 71,169)( 72,161)( 73,195)( 74,180)( 75,165)( 76,150)( 77,184)( 78,176)( 79,168)( 80,153)( 81,187)( 82,172)( 83,157)( 84,191)( 85,183)( 86,175)( 87,160)( 88,194)( 89,179)( 90,164)( 91,149)( 92,190)( 93,182)( 94,167)( 95,152)( 96,186)( 97,171)( 98,156)( 99,246)(100,287)(101,272)(102,257)(103,291)(104,276)(105,261)(106,253)(107,294)(108,279)(109,264)(110,249)(111,283)(112,268)(113,260)(114,252)(115,286)(116,271)(117,256)(118,290)(119,275)(120,267)(121,259)(122,293)(123,278)(124,263)(125,248)(126,282)(127,274)(128,266)(129,251)(130,285)(131,270)(132,255)(133,289)(134,281)(135,273)(136,258)(137,292)(138,277)(139,262)(140,247)(141,288)(142,280)(143,265)(144,250)(145,284)(146,269)(147,254);;
s2 := (  1, 11)(  2, 10)(  3,  9)(  4,  8)(  5, 14)(  6, 13)(  7, 12)( 15, 46)( 16, 45)( 17, 44)( 18, 43)( 19, 49)( 20, 48)( 21, 47)( 22, 39)( 23, 38)( 24, 37)( 25, 36)( 26, 42)( 27, 41)( 28, 40)( 29, 32)( 30, 31)( 33, 35)( 50, 60)( 51, 59)( 52, 58)( 53, 57)( 54, 63)( 55, 62)( 56, 61)( 64, 95)( 65, 94)( 66, 93)( 67, 92)( 68, 98)( 69, 97)( 70, 96)( 71, 88)( 72, 87)( 73, 86)( 74, 85)( 75, 91)( 76, 90)( 77, 89)( 78, 81)( 79, 80)( 82, 84)( 99,109)(100,108)(101,107)(102,106)(103,112)(104,111)(105,110)(113,144)(114,143)(115,142)(116,141)(117,147)(118,146)(119,145)(120,137)(121,136)(122,135)(123,134)(124,140)(125,139)(126,138)(127,130)(128,129)(131,133)(148,158)(149,157)(150,156)(151,155)(152,161)(153,160)(154,159)(162,193)(163,192)(164,191)(165,190)(166,196)(167,195)(168,194)(169,186)(170,185)(171,184)(172,183)(173,189)(174,188)(175,187)(176,179)(177,178)(180,182)(197,207)(198,206)(199,205)(200,204)(201,210)(202,209)(203,208)(211,242)(212,241)(213,240)(214,239)(215,245)(216,244)(217,243)(218,235)(219,234)(220,233)(221,232)(222,238)(223,237)(224,236)(225,228)(226,227)(229,231)(246,256)(247,255)(248,254)(249,253)(250,259)(251,258)(252,257)(260,291)(261,290)(262,289)(263,288)(264,294)(265,293)(266,292)(267,284)(268,283)(269,282)(270,281)(271,287)(272,286)(273,285)(274,277)(275,276)(278,280);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(294)!(  2, 46)(  3, 42)(  4, 31)(  5, 27)(  6, 16)(  7, 12)(  8, 30)(  9, 26)( 10, 15)( 13, 45)( 14, 41)( 17, 44)( 18, 40)( 19, 29)( 20, 25)( 22, 39)( 23, 35)( 28, 43)( 32, 49)( 33, 38)( 36, 48)( 50, 99)( 51,144)( 52,140)( 53,129)( 54,125)( 55,114)( 56,110)( 57,128)( 58,124)( 59,113)( 60,109)( 61,105)( 62,143)( 63,139)( 64,108)( 65,104)( 66,142)( 67,138)( 68,127)( 69,123)( 70,119)( 71,137)( 72,133)( 73,122)( 74,118)( 75,107)( 76,103)( 77,141)( 78,117)( 79,106)( 80,102)( 81,147)( 82,136)( 83,132)( 84,121)( 85,146)( 86,135)( 87,131)( 88,120)( 89,116)( 90,112)( 91,101)( 92,126)( 93,115)( 94,111)( 95,100)( 96,145)( 97,134)( 98,130)(149,193)(150,189)(151,178)(152,174)(153,163)(154,159)(155,177)(156,173)(157,162)(160,192)(161,188)(164,191)(165,187)(166,176)(167,172)(169,186)(170,182)(175,190)(179,196)(180,185)(183,195)(197,246)(198,291)(199,287)(200,276)(201,272)(202,261)(203,257)(204,275)(205,271)(206,260)(207,256)(208,252)(209,290)(210,286)(211,255)(212,251)(213,289)(214,285)(215,274)(216,270)(217,266)(218,284)(219,280)(220,269)(221,265)(222,254)(223,250)(224,288)(225,264)(226,253)(227,249)(228,294)(229,283)(230,279)(231,268)(232,293)(233,282)(234,278)(235,267)(236,263)(237,259)(238,248)(239,273)(240,262)(241,258)(242,247)(243,292)(244,281)(245,277);
s1 := Sym(294)!(  1,197)(  2,238)(  3,223)(  4,208)(  5,242)(  6,227)(  7,212)(  8,204)(  9,245)( 10,230)( 11,215)( 12,200)( 13,234)( 14,219)( 15,211)( 16,203)( 17,237)( 18,222)( 19,207)( 20,241)( 21,226)( 22,218)( 23,210)( 24,244)( 25,229)( 26,214)( 27,199)( 28,233)( 29,225)( 30,217)( 31,202)( 32,236)( 33,221)( 34,206)( 35,240)( 36,232)( 37,224)( 38,209)( 39,243)( 40,228)( 41,213)( 42,198)( 43,239)( 44,231)( 45,216)( 46,201)( 47,235)( 48,220)( 49,205)( 50,148)( 51,189)( 52,174)( 53,159)( 54,193)( 55,178)( 56,163)( 57,155)( 58,196)( 59,181)( 60,166)( 61,151)( 62,185)( 63,170)( 64,162)( 65,154)( 66,188)( 67,173)( 68,158)( 69,192)( 70,177)( 71,169)( 72,161)( 73,195)( 74,180)( 75,165)( 76,150)( 77,184)( 78,176)( 79,168)( 80,153)( 81,187)( 82,172)( 83,157)( 84,191)( 85,183)( 86,175)( 87,160)( 88,194)( 89,179)( 90,164)( 91,149)( 92,190)( 93,182)( 94,167)( 95,152)( 96,186)( 97,171)( 98,156)( 99,246)(100,287)(101,272)(102,257)(103,291)(104,276)(105,261)(106,253)(107,294)(108,279)(109,264)(110,249)(111,283)(112,268)(113,260)(114,252)(115,286)(116,271)(117,256)(118,290)(119,275)(120,267)(121,259)(122,293)(123,278)(124,263)(125,248)(126,282)(127,274)(128,266)(129,251)(130,285)(131,270)(132,255)(133,289)(134,281)(135,273)(136,258)(137,292)(138,277)(139,262)(140,247)(141,288)(142,280)(143,265)(144,250)(145,284)(146,269)(147,254);
s2 := Sym(294)!(  1, 11)(  2, 10)(  3,  9)(  4,  8)(  5, 14)(  6, 13)(  7, 12)( 15, 46)( 16, 45)( 17, 44)( 18, 43)( 19, 49)( 20, 48)( 21, 47)( 22, 39)( 23, 38)( 24, 37)( 25, 36)( 26, 42)( 27, 41)( 28, 40)( 29, 32)( 30, 31)( 33, 35)( 50, 60)( 51, 59)( 52, 58)( 53, 57)( 54, 63)( 55, 62)( 56, 61)( 64, 95)( 65, 94)( 66, 93)( 67, 92)( 68, 98)( 69, 97)( 70, 96)( 71, 88)( 72, 87)( 73, 86)( 74, 85)( 75, 91)( 76, 90)( 77, 89)( 78, 81)( 79, 80)( 82, 84)( 99,109)(100,108)(101,107)(102,106)(103,112)(104,111)(105,110)(113,144)(114,143)(115,142)(116,141)(117,147)(118,146)(119,145)(120,137)(121,136)(122,135)(123,134)(124,140)(125,139)(126,138)(127,130)(128,129)(131,133)(148,158)(149,157)(150,156)(151,155)(152,161)(153,160)(154,159)(162,193)(163,192)(164,191)(165,190)(166,196)(167,195)(168,194)(169,186)(170,185)(171,184)(172,183)(173,189)(174,188)(175,187)(176,179)(177,178)(180,182)(197,207)(198,206)(199,205)(200,204)(201,210)(202,209)(203,208)(211,242)(212,241)(213,240)(214,239)(215,245)(216,244)(217,243)(218,235)(219,234)(220,233)(221,232)(222,238)(223,237)(224,236)(225,228)(226,227)(229,231)(246,256)(247,255)(248,254)(249,253)(250,259)(251,258)(252,257)(260,291)(261,290)(262,289)(263,288)(264,294)(265,293)(266,292)(267,284)(268,283)(269,282)(270,281)(271,287)(272,286)(273,285)(274,277)(275,276)(278,280);
poly := sub<Sym(294)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*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 >;

References : None.
to this polytope

Polytope of Type {6,14}

Twisty Puzzle