Polytope of Type {8,18} with group SmallGroup(1152,153992)

Overview

Group: SmallGroup(1152,153992)
Rank: 3
Schläfli Type: {8,18}
Vertices, edges, …: 32, 288, 72
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

Quotients maximal quotients in bold

2-fold

{4,18}*576a

3-fold

{8,6}*384b

6-fold

{4,6}*192a

8-fold

{4,18}*144b

16-fold

{4,9}*72

24-fold

{4,6}*48c

48-fold

{4,3}*24

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=<(s1*s2)^9> 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)^2*s0*(s1*s2)^2> of order 2

36 facets

36 of {8}*16

16 vertex figures

16 of {18}*36

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

18 facets

18 of {8}*16

8 vertex figures

8 of {18}*36

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

18 facets

18 of {8}*16

12 vertex figures

8 of {9}*18
4 of {18}*36

Representations

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