Part of the Atlas of Small Regular Polytopes

Polytope of Type {18,8}

Atlas Canonical Name {18,8}*1152b

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1152,153992)
Rank
3
Schläfli Type
{18,8}
Vertices, edges, …
72, 288, 32
Order of s0s1s2
18
Order of s0s1s2s1
4
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Non-Orientable
  • Self-Petrie

Quotients maximal quotients in bold

2-fold

3-fold

6-fold

8-fold

16-fold

24-fold

48-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<(s0*s1)^9> of order 2

20 facets

36 vertex figures

P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2> of order 2

16 facets

36 vertex figures

P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2, s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 4

8 facets

18 vertex figures

P/N, where N=<s0*s1*s2*s1*s0*(s1*s2)^2, (s0*s1)^9> of order 4

12 facets

18 vertex figures

Representations

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

References

None.

to this polytope.

Twisty Puzzle