Overview
- Group
- SmallGroup(1296,867)
- Rank
- 3
- Schläfli Type
- {12,18}
- Vertices, edges, …
- 36, 324, 54
- Order of s0s1s2
- 12
- Order of s0s1s2s1
- 18
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
9-fold
12-fold
18-fold
27-fold
36-fold
54-fold
81-fold
108-fold
162-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.
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 4, 6)( 7, 8)( 10, 19)( 11, 21)( 12, 20)( 13, 24)( 14, 23)( 15, 22)( 16, 26)( 17, 25)( 18, 27)( 28, 57)( 29, 56)( 30, 55)( 31, 59)( 32, 58)( 33, 60)( 34, 61)( 35, 63)( 36, 62)( 37, 75)( 38, 74)( 39, 73)( 40, 77)( 41, 76)( 42, 78)( 43, 79)( 44, 81)( 45, 80)( 46, 66)( 47, 65)( 48, 64)( 49, 68)( 50, 67)( 51, 69)( 52, 70)( 53, 72)( 54, 71)( 83, 84)( 85, 87)( 88, 89)( 91,100)( 92,102)( 93,101)( 94,105)( 95,104)( 96,103)( 97,107)( 98,106)( 99,108)(109,138)(110,137)(111,136)(112,140)(113,139)(114,141)(115,142)(116,144)(117,143)(118,156)(119,155)(120,154)(121,158)(122,157)(123,159)(124,160)(125,162)(126,161)(127,147)(128,146)(129,145)(130,149)(131,148)(132,150)(133,151)(134,153)(135,152)(163,244)(164,246)(165,245)(166,249)(167,248)(168,247)(169,251)(170,250)(171,252)(172,262)(173,264)(174,263)(175,267)(176,266)(177,265)(178,269)(179,268)(180,270)(181,253)(182,255)(183,254)(184,258)(185,257)(186,256)(187,260)(188,259)(189,261)(190,300)(191,299)(192,298)(193,302)(194,301)(195,303)(196,304)(197,306)(198,305)(199,318)(200,317)(201,316)(202,320)(203,319)(204,321)(205,322)(206,324)(207,323)(208,309)(209,308)(210,307)(211,311)(212,310)(213,312)(214,313)(215,315)(216,314)(217,273)(218,272)(219,271)(220,275)(221,274)(222,276)(223,277)(224,279)(225,278)(226,291)(227,290)(228,289)(229,293)(230,292)(231,294)(232,295)(233,297)(234,296)(235,282)(236,281)(237,280)(238,284)(239,283)(240,285)(241,286)(242,288)(243,287);; s1 := ( 1,229)( 2,231)( 3,230)( 4,232)( 5,234)( 6,233)( 7,226)( 8,228)( 9,227)( 10,223)( 11,225)( 12,224)( 13,217)( 14,219)( 15,218)( 16,220)( 17,222)( 18,221)( 19,237)( 20,236)( 21,235)( 22,240)( 23,239)( 24,238)( 25,243)( 26,242)( 27,241)( 28,202)( 29,204)( 30,203)( 31,205)( 32,207)( 33,206)( 34,199)( 35,201)( 36,200)( 37,196)( 38,198)( 39,197)( 40,190)( 41,192)( 42,191)( 43,193)( 44,195)( 45,194)( 46,210)( 47,209)( 48,208)( 49,213)( 50,212)( 51,211)( 52,216)( 53,215)( 54,214)( 55,175)( 56,177)( 57,176)( 58,178)( 59,180)( 60,179)( 61,172)( 62,174)( 63,173)( 64,169)( 65,171)( 66,170)( 67,163)( 68,165)( 69,164)( 70,166)( 71,168)( 72,167)( 73,183)( 74,182)( 75,181)( 76,186)( 77,185)( 78,184)( 79,189)( 80,188)( 81,187)( 82,310)( 83,312)( 84,311)( 85,313)( 86,315)( 87,314)( 88,307)( 89,309)( 90,308)( 91,304)( 92,306)( 93,305)( 94,298)( 95,300)( 96,299)( 97,301)( 98,303)( 99,302)(100,318)(101,317)(102,316)(103,321)(104,320)(105,319)(106,324)(107,323)(108,322)(109,283)(110,285)(111,284)(112,286)(113,288)(114,287)(115,280)(116,282)(117,281)(118,277)(119,279)(120,278)(121,271)(122,273)(123,272)(124,274)(125,276)(126,275)(127,291)(128,290)(129,289)(130,294)(131,293)(132,292)(133,297)(134,296)(135,295)(136,256)(137,258)(138,257)(139,259)(140,261)(141,260)(142,253)(143,255)(144,254)(145,250)(146,252)(147,251)(148,244)(149,246)(150,245)(151,247)(152,249)(153,248)(154,264)(155,263)(156,262)(157,267)(158,266)(159,265)(160,270)(161,269)(162,268);; s2 := ( 2, 3)( 4, 7)( 5, 9)( 6, 8)( 11, 12)( 13, 16)( 14, 18)( 15, 17)( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 28, 57)( 29, 56)( 30, 55)( 31, 63)( 32, 62)( 33, 61)( 34, 60)( 35, 59)( 36, 58)( 37, 66)( 38, 65)( 39, 64)( 40, 72)( 41, 71)( 42, 70)( 43, 69)( 44, 68)( 45, 67)( 46, 75)( 47, 74)( 48, 73)( 49, 81)( 50, 80)( 51, 79)( 52, 78)( 53, 77)( 54, 76)( 83, 84)( 85, 88)( 86, 90)( 87, 89)( 92, 93)( 94, 97)( 95, 99)( 96, 98)(101,102)(103,106)(104,108)(105,107)(109,138)(110,137)(111,136)(112,144)(113,143)(114,142)(115,141)(116,140)(117,139)(118,147)(119,146)(120,145)(121,153)(122,152)(123,151)(124,150)(125,149)(126,148)(127,156)(128,155)(129,154)(130,162)(131,161)(132,160)(133,159)(134,158)(135,157)(164,165)(166,169)(167,171)(168,170)(173,174)(175,178)(176,180)(177,179)(182,183)(184,187)(185,189)(186,188)(190,219)(191,218)(192,217)(193,225)(194,224)(195,223)(196,222)(197,221)(198,220)(199,228)(200,227)(201,226)(202,234)(203,233)(204,232)(205,231)(206,230)(207,229)(208,237)(209,236)(210,235)(211,243)(212,242)(213,241)(214,240)(215,239)(216,238)(245,246)(247,250)(248,252)(249,251)(254,255)(256,259)(257,261)(258,260)(263,264)(265,268)(266,270)(267,269)(271,300)(272,299)(273,298)(274,306)(275,305)(276,304)(277,303)(278,302)(279,301)(280,309)(281,308)(282,307)(283,315)(284,314)(285,313)(286,312)(287,311)(288,310)(289,318)(290,317)(291,316)(292,324)(293,323)(294,322)(295,321)(296,320)(297,319);; 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*s2*s1*s0*s1*s0*s1*s2*s1,
s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s0,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(324)!( 2, 3)( 4, 6)( 7, 8)( 10, 19)( 11, 21)( 12, 20)( 13, 24)( 14, 23)( 15, 22)( 16, 26)( 17, 25)( 18, 27)( 28, 57)( 29, 56)( 30, 55)( 31, 59)( 32, 58)( 33, 60)( 34, 61)( 35, 63)( 36, 62)( 37, 75)( 38, 74)( 39, 73)( 40, 77)( 41, 76)( 42, 78)( 43, 79)( 44, 81)( 45, 80)( 46, 66)( 47, 65)( 48, 64)( 49, 68)( 50, 67)( 51, 69)( 52, 70)( 53, 72)( 54, 71)( 83, 84)( 85, 87)( 88, 89)( 91,100)( 92,102)( 93,101)( 94,105)( 95,104)( 96,103)( 97,107)( 98,106)( 99,108)(109,138)(110,137)(111,136)(112,140)(113,139)(114,141)(115,142)(116,144)(117,143)(118,156)(119,155)(120,154)(121,158)(122,157)(123,159)(124,160)(125,162)(126,161)(127,147)(128,146)(129,145)(130,149)(131,148)(132,150)(133,151)(134,153)(135,152)(163,244)(164,246)(165,245)(166,249)(167,248)(168,247)(169,251)(170,250)(171,252)(172,262)(173,264)(174,263)(175,267)(176,266)(177,265)(178,269)(179,268)(180,270)(181,253)(182,255)(183,254)(184,258)(185,257)(186,256)(187,260)(188,259)(189,261)(190,300)(191,299)(192,298)(193,302)(194,301)(195,303)(196,304)(197,306)(198,305)(199,318)(200,317)(201,316)(202,320)(203,319)(204,321)(205,322)(206,324)(207,323)(208,309)(209,308)(210,307)(211,311)(212,310)(213,312)(214,313)(215,315)(216,314)(217,273)(218,272)(219,271)(220,275)(221,274)(222,276)(223,277)(224,279)(225,278)(226,291)(227,290)(228,289)(229,293)(230,292)(231,294)(232,295)(233,297)(234,296)(235,282)(236,281)(237,280)(238,284)(239,283)(240,285)(241,286)(242,288)(243,287); s1 := Sym(324)!( 1,229)( 2,231)( 3,230)( 4,232)( 5,234)( 6,233)( 7,226)( 8,228)( 9,227)( 10,223)( 11,225)( 12,224)( 13,217)( 14,219)( 15,218)( 16,220)( 17,222)( 18,221)( 19,237)( 20,236)( 21,235)( 22,240)( 23,239)( 24,238)( 25,243)( 26,242)( 27,241)( 28,202)( 29,204)( 30,203)( 31,205)( 32,207)( 33,206)( 34,199)( 35,201)( 36,200)( 37,196)( 38,198)( 39,197)( 40,190)( 41,192)( 42,191)( 43,193)( 44,195)( 45,194)( 46,210)( 47,209)( 48,208)( 49,213)( 50,212)( 51,211)( 52,216)( 53,215)( 54,214)( 55,175)( 56,177)( 57,176)( 58,178)( 59,180)( 60,179)( 61,172)( 62,174)( 63,173)( 64,169)( 65,171)( 66,170)( 67,163)( 68,165)( 69,164)( 70,166)( 71,168)( 72,167)( 73,183)( 74,182)( 75,181)( 76,186)( 77,185)( 78,184)( 79,189)( 80,188)( 81,187)( 82,310)( 83,312)( 84,311)( 85,313)( 86,315)( 87,314)( 88,307)( 89,309)( 90,308)( 91,304)( 92,306)( 93,305)( 94,298)( 95,300)( 96,299)( 97,301)( 98,303)( 99,302)(100,318)(101,317)(102,316)(103,321)(104,320)(105,319)(106,324)(107,323)(108,322)(109,283)(110,285)(111,284)(112,286)(113,288)(114,287)(115,280)(116,282)(117,281)(118,277)(119,279)(120,278)(121,271)(122,273)(123,272)(124,274)(125,276)(126,275)(127,291)(128,290)(129,289)(130,294)(131,293)(132,292)(133,297)(134,296)(135,295)(136,256)(137,258)(138,257)(139,259)(140,261)(141,260)(142,253)(143,255)(144,254)(145,250)(146,252)(147,251)(148,244)(149,246)(150,245)(151,247)(152,249)(153,248)(154,264)(155,263)(156,262)(157,267)(158,266)(159,265)(160,270)(161,269)(162,268); s2 := Sym(324)!( 2, 3)( 4, 7)( 5, 9)( 6, 8)( 11, 12)( 13, 16)( 14, 18)( 15, 17)( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 28, 57)( 29, 56)( 30, 55)( 31, 63)( 32, 62)( 33, 61)( 34, 60)( 35, 59)( 36, 58)( 37, 66)( 38, 65)( 39, 64)( 40, 72)( 41, 71)( 42, 70)( 43, 69)( 44, 68)( 45, 67)( 46, 75)( 47, 74)( 48, 73)( 49, 81)( 50, 80)( 51, 79)( 52, 78)( 53, 77)( 54, 76)( 83, 84)( 85, 88)( 86, 90)( 87, 89)( 92, 93)( 94, 97)( 95, 99)( 96, 98)(101,102)(103,106)(104,108)(105,107)(109,138)(110,137)(111,136)(112,144)(113,143)(114,142)(115,141)(116,140)(117,139)(118,147)(119,146)(120,145)(121,153)(122,152)(123,151)(124,150)(125,149)(126,148)(127,156)(128,155)(129,154)(130,162)(131,161)(132,160)(133,159)(134,158)(135,157)(164,165)(166,169)(167,171)(168,170)(173,174)(175,178)(176,180)(177,179)(182,183)(184,187)(185,189)(186,188)(190,219)(191,218)(192,217)(193,225)(194,224)(195,223)(196,222)(197,221)(198,220)(199,228)(200,227)(201,226)(202,234)(203,233)(204,232)(205,231)(206,230)(207,229)(208,237)(209,236)(210,235)(211,243)(212,242)(213,241)(214,240)(215,239)(216,238)(245,246)(247,250)(248,252)(249,251)(254,255)(256,259)(257,261)(258,260)(263,264)(265,268)(266,270)(267,269)(271,300)(272,299)(273,298)(274,306)(275,305)(276,304)(277,303)(278,302)(279,301)(280,309)(281,308)(282,307)(283,315)(284,314)(285,313)(286,312)(287,311)(288,310)(289,318)(290,317)(291,316)(292,324)(293,323)(294,322)(295,321)(296,320)(297,319); poly := sub<Sym(324)|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*s2*s1*s0*s1*s0*s1*s2*s1, s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s0, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1 >;
References
None.
to this polytope.