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}*1152f
if this polytope has a name.
Group : SmallGroup(1152,154295)
Rank : 3
Schlafli Type : {8,18}
Number of vertices, edges, etc : 32, 288, 72
Order of s₀s₁s₂ : 36
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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}*576b, {8,18}*576b, {8,18}*576c
   3-fold quotients : {8,6}*384f
   4-fold quotients : {8,9}*288, {4,18}*288
   6-fold quotients : {4,6}*192b, {8,6}*192b, {8,6}*192c
   8-fold quotients : {4,18}*144a, {4,9}*144, {4,18}*144b, {4,18}*144c
   12-fold quotients : {8,3}*96, {4,6}*96
   16-fold quotients : {4,9}*72, {2,18}*72
   24-fold quotients : {4,6}*48a, {4,3}*48, {4,6}*48b, {4,6}*48c
   32-fold quotients : {2,9}*36
   48-fold quotients : {4,3}*24, {2,6}*24
   72-fold quotients : {4,2}*16
   96-fold quotients : {2,3}*12
   144-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=<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
      24 vertex figures:
         16 of {9}*18
         8 of {18}*36

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {8,18}

Twisty Puzzle