Polytope of Type {8,18}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,18}*1152c
if this polytope has a name.
Group : SmallGroup(1152,153992)
Rank : 3
Schlafli Type : {8,18}
Number of vertices, edges, etc : 32, 288, 72
Order of s₀s₁s₂ : 18
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
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 : {4,18}*576a
   3-fold quotients : {8,6}*384c
   6-fold quotients : {4,6}*192a
   8-fold quotients : {4,18}*144b
   16-fold quotients : {4,9}*72
   24-fold quotients : {4,6}*48c
   48-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 2.
      36 facets:
         36 of {8}*16
      20 vertex figures:
         8 of {9}*18
         12 of {18}*36
   P/N, where N=<s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2> of order 2.
      36 facets:
         36 of {8}*16
      16 vertex figures:
         16 of {18}*36
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*s1*s0*s2*s1> of order 4.
      18 facets:
         18 of {8}*16
      8 vertex figures:
         8 of {18}*36
   P/N, where N=<s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 4.
      18 facets:
         18 of {8}*16
      12 vertex figures:
         8 of {9}*18
         4 of {18}*36

Permutation Representation (GAP) :

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

Polytope of Type {8,18}

Twisty Puzzle