Overview
- Group
- SmallGroup(1344,11343)
- Rank
- 3
- Schläfli Type
- {6,42}
- Vertices, edges, …
- 16, 336, 112
- Order of s0s1s2
- 56
- Order of s0s1s2s1
- 12
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
2-fold
4-fold
7-fold
14-fold
24-fold
28-fold
48-fold
56-fold
168-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*s0*s2*s1*s0*(s2*s1)^4*s0*s2*s1*s2> of order 2
56 facets
- 56 of {6}*12
12 vertex figures
Representations
Permutation Representation (GAP)
s0 := ( 3, 4)( 5, 7)( 6, 8)( 11, 12)( 13, 15)( 14, 16)( 19, 20)( 21, 23)( 22, 24)( 27, 28)( 29, 31)( 30, 32)( 35, 36)( 37, 39)( 38, 40)( 43, 44)( 45, 47)( 46, 48)( 51, 52)( 53, 55)( 54, 56)( 57,113)( 58,114)( 59,116)( 60,115)( 61,119)( 62,120)( 63,117)( 64,118)( 65,121)( 66,122)( 67,124)( 68,123)( 69,127)( 70,128)( 71,125)( 72,126)( 73,129)( 74,130)( 75,132)( 76,131)( 77,135)( 78,136)( 79,133)( 80,134)( 81,137)( 82,138)( 83,140)( 84,139)( 85,143)( 86,144)( 87,141)( 88,142)( 89,145)( 90,146)( 91,148)( 92,147)( 93,151)( 94,152)( 95,149)( 96,150)( 97,153)( 98,154)( 99,156)(100,155)(101,159)(102,160)(103,157)(104,158)(105,161)(106,162)(107,164)(108,163)(109,167)(110,168)(111,165)(112,166)(169,170)(173,176)(174,175)(177,178)(181,184)(182,183)(185,186)(189,192)(190,191)(193,194)(197,200)(198,199)(201,202)(205,208)(206,207)(209,210)(213,216)(214,215)(217,218)(221,224)(222,223)(225,282)(226,281)(227,283)(228,284)(229,288)(230,287)(231,286)(232,285)(233,290)(234,289)(235,291)(236,292)(237,296)(238,295)(239,294)(240,293)(241,298)(242,297)(243,299)(244,300)(245,304)(246,303)(247,302)(248,301)(249,306)(250,305)(251,307)(252,308)(253,312)(254,311)(255,310)(256,309)(257,314)(258,313)(259,315)(260,316)(261,320)(262,319)(263,318)(264,317)(265,322)(266,321)(267,323)(268,324)(269,328)(270,327)(271,326)(272,325)(273,330)(274,329)(275,331)(276,332)(277,336)(278,335)(279,334)(280,333);; s1 := ( 1, 57)( 2, 58)( 3, 63)( 4, 64)( 5, 62)( 6, 61)( 7, 59)( 8, 60)( 9,105)( 10,106)( 11,111)( 12,112)( 13,110)( 14,109)( 15,107)( 16,108)( 17, 97)( 18, 98)( 19,103)( 20,104)( 21,102)( 22,101)( 23, 99)( 24,100)( 25, 89)( 26, 90)( 27, 95)( 28, 96)( 29, 94)( 30, 93)( 31, 91)( 32, 92)( 33, 81)( 34, 82)( 35, 87)( 36, 88)( 37, 86)( 38, 85)( 39, 83)( 40, 84)( 41, 73)( 42, 74)( 43, 79)( 44, 80)( 45, 78)( 46, 77)( 47, 75)( 48, 76)( 49, 65)( 50, 66)( 51, 71)( 52, 72)( 53, 70)( 54, 69)( 55, 67)( 56, 68)(115,119)(116,120)(117,118)(121,161)(122,162)(123,167)(124,168)(125,166)(126,165)(127,163)(128,164)(129,153)(130,154)(131,159)(132,160)(133,158)(134,157)(135,155)(136,156)(137,145)(138,146)(139,151)(140,152)(141,150)(142,149)(143,147)(144,148)(169,225)(170,226)(171,231)(172,232)(173,230)(174,229)(175,227)(176,228)(177,273)(178,274)(179,279)(180,280)(181,278)(182,277)(183,275)(184,276)(185,265)(186,266)(187,271)(188,272)(189,270)(190,269)(191,267)(192,268)(193,257)(194,258)(195,263)(196,264)(197,262)(198,261)(199,259)(200,260)(201,249)(202,250)(203,255)(204,256)(205,254)(206,253)(207,251)(208,252)(209,241)(210,242)(211,247)(212,248)(213,246)(214,245)(215,243)(216,244)(217,233)(218,234)(219,239)(220,240)(221,238)(222,237)(223,235)(224,236)(283,287)(284,288)(285,286)(289,329)(290,330)(291,335)(292,336)(293,334)(294,333)(295,331)(296,332)(297,321)(298,322)(299,327)(300,328)(301,326)(302,325)(303,323)(304,324)(305,313)(306,314)(307,319)(308,320)(309,318)(310,317)(311,315)(312,316);; s2 := ( 1,179)( 2,180)( 3,177)( 4,178)( 5,182)( 6,181)( 7,183)( 8,184)( 9,171)( 10,172)( 11,169)( 12,170)( 13,174)( 14,173)( 15,175)( 16,176)( 17,219)( 18,220)( 19,217)( 20,218)( 21,222)( 22,221)( 23,223)( 24,224)( 25,211)( 26,212)( 27,209)( 28,210)( 29,214)( 30,213)( 31,215)( 32,216)( 33,203)( 34,204)( 35,201)( 36,202)( 37,206)( 38,205)( 39,207)( 40,208)( 41,195)( 42,196)( 43,193)( 44,194)( 45,198)( 46,197)( 47,199)( 48,200)( 49,187)( 50,188)( 51,185)( 52,186)( 53,190)( 54,189)( 55,191)( 56,192)( 57,291)( 58,292)( 59,289)( 60,290)( 61,294)( 62,293)( 63,295)( 64,296)( 65,283)( 66,284)( 67,281)( 68,282)( 69,286)( 70,285)( 71,287)( 72,288)( 73,331)( 74,332)( 75,329)( 76,330)( 77,334)( 78,333)( 79,335)( 80,336)( 81,323)( 82,324)( 83,321)( 84,322)( 85,326)( 86,325)( 87,327)( 88,328)( 89,315)( 90,316)( 91,313)( 92,314)( 93,318)( 94,317)( 95,319)( 96,320)( 97,307)( 98,308)( 99,305)(100,306)(101,310)(102,309)(103,311)(104,312)(105,299)(106,300)(107,297)(108,298)(109,302)(110,301)(111,303)(112,304)(113,235)(114,236)(115,233)(116,234)(117,238)(118,237)(119,239)(120,240)(121,227)(122,228)(123,225)(124,226)(125,230)(126,229)(127,231)(128,232)(129,275)(130,276)(131,273)(132,274)(133,278)(134,277)(135,279)(136,280)(137,267)(138,268)(139,265)(140,266)(141,270)(142,269)(143,271)(144,272)(145,259)(146,260)(147,257)(148,258)(149,262)(150,261)(151,263)(152,264)(153,251)(154,252)(155,249)(156,250)(157,254)(158,253)(159,255)(160,256)(161,243)(162,244)(163,241)(164,242)(165,246)(166,245)(167,247)(168,248);; 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*s2*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*s0*s1,
s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s0,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(336)!( 3, 4)( 5, 7)( 6, 8)( 11, 12)( 13, 15)( 14, 16)( 19, 20)( 21, 23)( 22, 24)( 27, 28)( 29, 31)( 30, 32)( 35, 36)( 37, 39)( 38, 40)( 43, 44)( 45, 47)( 46, 48)( 51, 52)( 53, 55)( 54, 56)( 57,113)( 58,114)( 59,116)( 60,115)( 61,119)( 62,120)( 63,117)( 64,118)( 65,121)( 66,122)( 67,124)( 68,123)( 69,127)( 70,128)( 71,125)( 72,126)( 73,129)( 74,130)( 75,132)( 76,131)( 77,135)( 78,136)( 79,133)( 80,134)( 81,137)( 82,138)( 83,140)( 84,139)( 85,143)( 86,144)( 87,141)( 88,142)( 89,145)( 90,146)( 91,148)( 92,147)( 93,151)( 94,152)( 95,149)( 96,150)( 97,153)( 98,154)( 99,156)(100,155)(101,159)(102,160)(103,157)(104,158)(105,161)(106,162)(107,164)(108,163)(109,167)(110,168)(111,165)(112,166)(169,170)(173,176)(174,175)(177,178)(181,184)(182,183)(185,186)(189,192)(190,191)(193,194)(197,200)(198,199)(201,202)(205,208)(206,207)(209,210)(213,216)(214,215)(217,218)(221,224)(222,223)(225,282)(226,281)(227,283)(228,284)(229,288)(230,287)(231,286)(232,285)(233,290)(234,289)(235,291)(236,292)(237,296)(238,295)(239,294)(240,293)(241,298)(242,297)(243,299)(244,300)(245,304)(246,303)(247,302)(248,301)(249,306)(250,305)(251,307)(252,308)(253,312)(254,311)(255,310)(256,309)(257,314)(258,313)(259,315)(260,316)(261,320)(262,319)(263,318)(264,317)(265,322)(266,321)(267,323)(268,324)(269,328)(270,327)(271,326)(272,325)(273,330)(274,329)(275,331)(276,332)(277,336)(278,335)(279,334)(280,333); s1 := Sym(336)!( 1, 57)( 2, 58)( 3, 63)( 4, 64)( 5, 62)( 6, 61)( 7, 59)( 8, 60)( 9,105)( 10,106)( 11,111)( 12,112)( 13,110)( 14,109)( 15,107)( 16,108)( 17, 97)( 18, 98)( 19,103)( 20,104)( 21,102)( 22,101)( 23, 99)( 24,100)( 25, 89)( 26, 90)( 27, 95)( 28, 96)( 29, 94)( 30, 93)( 31, 91)( 32, 92)( 33, 81)( 34, 82)( 35, 87)( 36, 88)( 37, 86)( 38, 85)( 39, 83)( 40, 84)( 41, 73)( 42, 74)( 43, 79)( 44, 80)( 45, 78)( 46, 77)( 47, 75)( 48, 76)( 49, 65)( 50, 66)( 51, 71)( 52, 72)( 53, 70)( 54, 69)( 55, 67)( 56, 68)(115,119)(116,120)(117,118)(121,161)(122,162)(123,167)(124,168)(125,166)(126,165)(127,163)(128,164)(129,153)(130,154)(131,159)(132,160)(133,158)(134,157)(135,155)(136,156)(137,145)(138,146)(139,151)(140,152)(141,150)(142,149)(143,147)(144,148)(169,225)(170,226)(171,231)(172,232)(173,230)(174,229)(175,227)(176,228)(177,273)(178,274)(179,279)(180,280)(181,278)(182,277)(183,275)(184,276)(185,265)(186,266)(187,271)(188,272)(189,270)(190,269)(191,267)(192,268)(193,257)(194,258)(195,263)(196,264)(197,262)(198,261)(199,259)(200,260)(201,249)(202,250)(203,255)(204,256)(205,254)(206,253)(207,251)(208,252)(209,241)(210,242)(211,247)(212,248)(213,246)(214,245)(215,243)(216,244)(217,233)(218,234)(219,239)(220,240)(221,238)(222,237)(223,235)(224,236)(283,287)(284,288)(285,286)(289,329)(290,330)(291,335)(292,336)(293,334)(294,333)(295,331)(296,332)(297,321)(298,322)(299,327)(300,328)(301,326)(302,325)(303,323)(304,324)(305,313)(306,314)(307,319)(308,320)(309,318)(310,317)(311,315)(312,316); s2 := Sym(336)!( 1,179)( 2,180)( 3,177)( 4,178)( 5,182)( 6,181)( 7,183)( 8,184)( 9,171)( 10,172)( 11,169)( 12,170)( 13,174)( 14,173)( 15,175)( 16,176)( 17,219)( 18,220)( 19,217)( 20,218)( 21,222)( 22,221)( 23,223)( 24,224)( 25,211)( 26,212)( 27,209)( 28,210)( 29,214)( 30,213)( 31,215)( 32,216)( 33,203)( 34,204)( 35,201)( 36,202)( 37,206)( 38,205)( 39,207)( 40,208)( 41,195)( 42,196)( 43,193)( 44,194)( 45,198)( 46,197)( 47,199)( 48,200)( 49,187)( 50,188)( 51,185)( 52,186)( 53,190)( 54,189)( 55,191)( 56,192)( 57,291)( 58,292)( 59,289)( 60,290)( 61,294)( 62,293)( 63,295)( 64,296)( 65,283)( 66,284)( 67,281)( 68,282)( 69,286)( 70,285)( 71,287)( 72,288)( 73,331)( 74,332)( 75,329)( 76,330)( 77,334)( 78,333)( 79,335)( 80,336)( 81,323)( 82,324)( 83,321)( 84,322)( 85,326)( 86,325)( 87,327)( 88,328)( 89,315)( 90,316)( 91,313)( 92,314)( 93,318)( 94,317)( 95,319)( 96,320)( 97,307)( 98,308)( 99,305)(100,306)(101,310)(102,309)(103,311)(104,312)(105,299)(106,300)(107,297)(108,298)(109,302)(110,301)(111,303)(112,304)(113,235)(114,236)(115,233)(116,234)(117,238)(118,237)(119,239)(120,240)(121,227)(122,228)(123,225)(124,226)(125,230)(126,229)(127,231)(128,232)(129,275)(130,276)(131,273)(132,274)(133,278)(134,277)(135,279)(136,280)(137,267)(138,268)(139,265)(140,266)(141,270)(142,269)(143,271)(144,272)(145,259)(146,260)(147,257)(148,258)(149,262)(150,261)(151,263)(152,264)(153,251)(154,252)(155,249)(156,250)(157,254)(158,253)(159,255)(160,256)(161,243)(162,244)(163,241)(164,242)(165,246)(166,245)(167,247)(168,248); poly := sub<Sym(336)|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*s2*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*s0*s1, s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s0, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1 >;
References
None.
to this polytope.