Overview
- Group
- SmallGroup(1152,157851)
- Rank
- 3
- Schläfli Type
- {12,6}
- Vertices, edges, …
- 96, 288, 48
- Order of s0s1s2
- 12
- Order of s0s1s2s1
- 12
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Self-Petrie
Quotients maximal quotients in bold
2-fold
4-fold
8-fold
12-fold
16-fold
24-fold
32-fold
48-fold
96-fold
144-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)^2*s0*s2*(s1*s0)^4*s2*s1*s0*s1> of order 2
24 facets
- 24 of {12}*24
48 vertex figures
- 48 of {6}*12
P/N, where N=<s0*s1*s2*(s1*s0)^3*s1*s2*s1> of order 2
24 facets
- 24 of {12}*24
48 vertex figures
- 48 of {6}*12
P/N, where N=<(s0*s1)^2*s2*(s1*s0)^5*s1*s2*s1> of order 2
24 facets
- 24 of {12}*24
48 vertex figures
- 48 of {6}*12
P/N, where N=<s0*s1*s0*s2*(s1*s0)^5*s2*s1*s2> of order 2
24 facets
- 24 of {12}*24
48 vertex figures
- 48 of {6}*12
P/N, where N=<(s0*s1)^2*s2*(s1*s0)^5*s2*s1*s2> of order 2
24 facets
- 24 of {12}*24
48 vertex figures
- 48 of {6}*12
P/N, where N=<s0*s1*s0*s2*(s1*s0)^5*s1*s2*s1> of order 2
24 facets
- 24 of {12}*24
48 vertex figures
- 48 of {6}*12
P/N, where N=<s0*s1*s2*(s1*s0)^3*s2*s1*s2> of order 2
24 facets
- 24 of {12}*24
48 vertex figures
- 48 of {6}*12
P/N, where N=<((s1*s0)^2*s1*s2)^3> of order 2
24 facets
- 24 of {12}*24
48 vertex figures
- 48 of {6}*12
P/N, where N=<(s0*s1)^3*s2*(s1*s0)^3*s2> of order 3
16 facets
- 16 of {12}*24
32 vertex figures
- 32 of {6}*12
P/N, where N=<(s0*s1)^6, s0*s1*s2*(s1*s0)^3*s2*s1*s2> of order 4
16 facets
24 vertex figures
- 24 of {6}*12
P/N, where N=<(s0*s1)^2*s0*s2*(s1*s0)^4*s2*s1*s0*s1, (s0*s1)^2*(s2*(s1*s0)^2*s1)^2*s2*s1> of order 4
12 facets
- 12 of {12}*24
24 vertex figures
- 24 of {6}*12
P/N, where N=<(s0*s1)^6, (s0*s1)^2*s2*(s1*s0)^5*s2*s1*s2> of order 4
16 facets
24 vertex figures
- 24 of {6}*12
P/N, where N=<s0*s1*s2*(s1*s0)^3*s1*s2*s1, (s1*s0*s2)^2*(s1*s0)^2*s1*s2> of order 4
12 facets
- 12 of {12}*24
24 vertex figures
- 24 of {6}*12
P/N, where N=<(s0*s1)^3*s2*s1*s0*s2*s1*s2, s0*s1*s2*(s1*s0)^3*s1*s2*s1> of order 4
12 facets
- 12 of {12}*24
24 vertex figures
- 24 of {6}*12
P/N, where N=<(s0*s1)^6, (s0*s1)^2*(s2*s1*s0)^2*s2*s1> of order 4
16 facets
24 vertex figures
- 24 of {6}*12
P/N, where N=<(s1*s0*s2)^2*(s1*s0)^2*s1*s2, s0*(s1*s0*s2)^2*(s1*s0)^3*s2> of order 4
12 facets
- 12 of {12}*24
24 vertex figures
- 24 of {6}*12
P/N, where N=<(s0*s1)^6, (s0*s1)^2*s2*(s1*s0)^5*s1*s2*s1> of order 4
16 facets
24 vertex figures
- 24 of {6}*12
P/N, where N=<(s0*s1)^4*(s0*s2*s1)^3, s0*s1*s0*s2*(s1*s0)^5*s1*s2*s1> of order 4
12 facets
- 12 of {12}*24
24 vertex figures
- 24 of {6}*12
P/N, where N=<(s0*s1)^6, s0*s1*s2*(s1*s0)^3*s1*s2*s1> of order 4
16 facets
24 vertex figures
- 24 of {6}*12
P/N, where N=<s1*s0*s1*s2*(s1*s0)^3*s1*s2, (s0*s1)^2*s2*(s1*s0)^4*s2> of order 4
12 facets
- 12 of {12}*24
24 vertex figures
- 24 of {6}*12
P/N, where N=<(s0*s1)^4*(s0*s2*s1)^3, s0*s1*s0*s2*(s1*s0)^5*s2*s1*s2> of order 4
12 facets
- 12 of {12}*24
24 vertex figures
- 24 of {6}*12
P/N, where N=<(s1*s0)^2*s1*s2*s1*s0*s2*s1*s2> of order 4
12 facets
- 12 of {12}*24
24 vertex figures
- 24 of {6}*12
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2, s0*s1*s2*(s1*s0)^3*s1*s2*s1> of order 4
12 facets
- 12 of {12}*24
24 vertex figures
- 24 of {6}*12
P/N, where N=<s0*s1*s0*s2*(s1*s0)^2*s2*s1, (s0*s1)^6> of order 4
16 facets
24 vertex figures
- 24 of {6}*12
P/N, where N=<(s0*s1)^5*s2*(s1*s0)^2*s2*s1, s0*s1*s0*s2*(s1*s0)^5*s1*s2*s1> of order 4
12 facets
- 12 of {12}*24
24 vertex figures
- 24 of {6}*12
P/N, where N=<(s1*s0)^2*s2*s1*s0*s1*s2> of order 4
12 facets
- 12 of {12}*24
24 vertex figures
- 24 of {6}*12
P/N, where N=<(s0*s1)^4*s2*s1*s0*s1*s2> of order 4
12 facets
- 12 of {12}*24
24 vertex figures
- 24 of {6}*12
P/N, where N=<(s0*s1)^3*(s0*s2*s1)^2*s2> of order 4
12 facets
- 12 of {12}*24
24 vertex figures
- 24 of {6}*12
P/N, where N=<(s0*s1)^4, (s0*s1)^2*s2*(s1*s0)^5*s1*s2> of order 6
12 facets
16 vertex figures
- 16 of {6}*12
P/N, where N=<(s0*s1)^3*s2*(s1*s0)^3*s2, (s0*s1)^5*s2*(s1*s0)^2*s2*s1*s2> of order 6
8 facets
- 8 of {12}*24
16 vertex figures
- 16 of {6}*12
P/N, where N=<(s0*s1)^3*s2*(s1*s0)^3*s2, (s0*s1)^5*s2*(s1*s0)^2*s1*s2*s1> of order 6
8 facets
- 8 of {12}*24
16 vertex figures
- 16 of {6}*12
P/N, where N=<(s0*s1)^4, s0*s1*s0*s2*(s1*s0)^5*s2*s1*s2> of order 6
12 facets
16 vertex figures
- 16 of {6}*12
P/N, where N=<s1*s0*s1*s2*(s1*s0)^3*s1*s2, (s0*s1)^3*(s0*s2*s1)^2*s2> of order 8
6 facets
- 6 of {12}*24
12 vertex figures
- 12 of {6}*12
P/N, where N=<(s1*s0)^2*s1*s2*s1*s0*s2*s1*s2, (s0*s1)^6> of order 8
8 facets
12 vertex figures
- 12 of {6}*12
P/N, where N=<(s0*s1)^6, s0*s1*s2*(s1*s0)^3*s1*s2*s1, s0*(s1*s0*s2)^2*(s1*s0)^2*s1*s2> of order 8
8 facets
12 vertex figures
- 12 of {6}*12
P/N, where N=<(s0*s1)^6, (s0*s1)^3*s2*s1*s0*s2*s1*s2, s0*s1*s2*(s1*s0)^3*s1*s2*s1> of order 8
8 facets
12 vertex figures
- 12 of {6}*12
P/N, where N=<s1*s0*s1*s2*(s1*s0)^3*s1*s2, (s0*s1)^4*s2*s1*s0*s1*s2> of order 8
6 facets
- 6 of {12}*24
12 vertex figures
- 12 of {6}*12
P/N, where N=<(s0*s1)^6, s0*s1*s2*(s1*s0)^3*s1*s2*s1, (s0*s1)^2*s2*(s1*s0)^3*s1*s2> of order 8
8 facets
12 vertex figures
- 12 of {6}*12
P/N, where N=<(s1*s0)^2*s2*s1*s0*s1*s2, (s0*s1)^6> of order 8
8 facets
12 vertex figures
- 12 of {6}*12
P/N, where N=<(s0*s1)^6, s0*s1*s2*(s1*s0)^3*s1*s2*s1, (s1*s0*s2)^2*(s1*s0)^2*s1*s2> of order 8
8 facets
12 vertex figures
- 12 of {6}*12
P/N, where N=<(s1*s0*s2)^2*(s1*s0)^2*s1*s2, (s0*s1)^3*(s0*s2*s1)^2*s2> of order 8
6 facets
- 6 of {12}*24
12 vertex figures
- 12 of {6}*12
P/N, where N=<(s1*s0*s2)^2*(s1*s0)^2*s1*s2, (s0*s1)^4*s2*s1*s0*s1*s2> of order 8
6 facets
- 6 of {12}*24
12 vertex figures
- 12 of {6}*12
P/N, where N=<(s1*s0)^2*s1*s2*s1*s0*s2*s1*s2, (s0*s1)^5*s2*(s1*s0)^2*s2*s1> of order 8
6 facets
- 6 of {12}*24
12 vertex figures
- 12 of {6}*12
P/N, where N=<(s1*s0)^2*s2*s1*s0*s1*s2, (s0*s1)^4*(s0*s2*s1)^3> of order 8
6 facets
- 6 of {12}*24
12 vertex figures
- 12 of {6}*12
P/N, where N=<s0*s1*s0*s2*(s1*s0)^2*s2*s1, (s0*s1)^6, s0*s1*(s2*s1*s0)^3*s1> of order 8
8 facets
12 vertex figures
- 12 of {6}*12
Representations
Permutation Representation (GAP)
s0 := ( 1, 9)( 2, 10)( 3, 12)( 4, 11)( 5, 13)( 6, 14)( 7, 16)( 8, 15)( 17, 25)( 18, 26)( 19, 28)( 20, 27)( 21, 29)( 22, 30)( 23, 32)( 24, 31)( 33, 41)( 34, 42)( 35, 44)( 36, 43)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 49,105)( 50,106)( 51,108)( 52,107)( 53,109)( 54,110)( 55,112)( 56,111)( 57, 97)( 58, 98)( 59,100)( 60, 99)( 61,101)( 62,102)( 63,104)( 64,103)( 65,121)( 66,122)( 67,124)( 68,123)( 69,125)( 70,126)( 71,128)( 72,127)( 73,113)( 74,114)( 75,116)( 76,115)( 77,117)( 78,118)( 79,120)( 80,119)( 81,137)( 82,138)( 83,140)( 84,139)( 85,141)( 86,142)( 87,144)( 88,143)( 89,129)( 90,130)( 91,132)( 92,131)( 93,133)( 94,134)( 95,136)( 96,135)(145,153)(146,154)(147,156)(148,155)(149,157)(150,158)(151,160)(152,159)(161,169)(162,170)(163,172)(164,171)(165,173)(166,174)(167,176)(168,175)(177,185)(178,186)(179,188)(180,187)(181,189)(182,190)(183,192)(184,191)(193,249)(194,250)(195,252)(196,251)(197,253)(198,254)(199,256)(200,255)(201,241)(202,242)(203,244)(204,243)(205,245)(206,246)(207,248)(208,247)(209,265)(210,266)(211,268)(212,267)(213,269)(214,270)(215,272)(216,271)(217,257)(218,258)(219,260)(220,259)(221,261)(222,262)(223,264)(224,263)(225,281)(226,282)(227,284)(228,283)(229,285)(230,286)(231,288)(232,287)(233,273)(234,274)(235,276)(236,275)(237,277)(238,278)(239,280)(240,279);; s1 := ( 1, 49)( 2, 52)( 3, 51)( 4, 50)( 5, 53)( 6, 56)( 7, 55)( 8, 54)( 9, 61)( 10, 64)( 11, 63)( 12, 62)( 13, 57)( 14, 60)( 15, 59)( 16, 58)( 17, 81)( 18, 84)( 19, 83)( 20, 82)( 21, 85)( 22, 88)( 23, 87)( 24, 86)( 25, 93)( 26, 96)( 27, 95)( 28, 94)( 29, 89)( 30, 92)( 31, 91)( 32, 90)( 33, 65)( 34, 68)( 35, 67)( 36, 66)( 37, 69)( 38, 72)( 39, 71)( 40, 70)( 41, 77)( 42, 80)( 43, 79)( 44, 78)( 45, 73)( 46, 76)( 47, 75)( 48, 74)( 98,100)(102,104)(105,109)(106,112)(107,111)(108,110)(113,129)(114,132)(115,131)(116,130)(117,133)(118,136)(119,135)(120,134)(121,141)(122,144)(123,143)(124,142)(125,137)(126,140)(127,139)(128,138)(145,193)(146,196)(147,195)(148,194)(149,197)(150,200)(151,199)(152,198)(153,205)(154,208)(155,207)(156,206)(157,201)(158,204)(159,203)(160,202)(161,225)(162,228)(163,227)(164,226)(165,229)(166,232)(167,231)(168,230)(169,237)(170,240)(171,239)(172,238)(173,233)(174,236)(175,235)(176,234)(177,209)(178,212)(179,211)(180,210)(181,213)(182,216)(183,215)(184,214)(185,221)(186,224)(187,223)(188,222)(189,217)(190,220)(191,219)(192,218)(242,244)(246,248)(249,253)(250,256)(251,255)(252,254)(257,273)(258,276)(259,275)(260,274)(261,277)(262,280)(263,279)(264,278)(265,285)(266,288)(267,287)(268,286)(269,281)(270,284)(271,283)(272,282);; s2 := ( 1,162)( 2,161)( 3,163)( 4,164)( 5,174)( 6,173)( 7,175)( 8,176)( 9,170)( 10,169)( 11,171)( 12,172)( 13,166)( 14,165)( 15,167)( 16,168)( 17,146)( 18,145)( 19,147)( 20,148)( 21,158)( 22,157)( 23,159)( 24,160)( 25,154)( 26,153)( 27,155)( 28,156)( 29,150)( 30,149)( 31,151)( 32,152)( 33,178)( 34,177)( 35,179)( 36,180)( 37,190)( 38,189)( 39,191)( 40,192)( 41,186)( 42,185)( 43,187)( 44,188)( 45,182)( 46,181)( 47,183)( 48,184)( 49,258)( 50,257)( 51,259)( 52,260)( 53,270)( 54,269)( 55,271)( 56,272)( 57,266)( 58,265)( 59,267)( 60,268)( 61,262)( 62,261)( 63,263)( 64,264)( 65,242)( 66,241)( 67,243)( 68,244)( 69,254)( 70,253)( 71,255)( 72,256)( 73,250)( 74,249)( 75,251)( 76,252)( 77,246)( 78,245)( 79,247)( 80,248)( 81,274)( 82,273)( 83,275)( 84,276)( 85,286)( 86,285)( 87,287)( 88,288)( 89,282)( 90,281)( 91,283)( 92,284)( 93,278)( 94,277)( 95,279)( 96,280)( 97,210)( 98,209)( 99,211)(100,212)(101,222)(102,221)(103,223)(104,224)(105,218)(106,217)(107,219)(108,220)(109,214)(110,213)(111,215)(112,216)(113,194)(114,193)(115,195)(116,196)(117,206)(118,205)(119,207)(120,208)(121,202)(122,201)(123,203)(124,204)(125,198)(126,197)(127,199)(128,200)(129,226)(130,225)(131,227)(132,228)(133,238)(134,237)(135,239)(136,240)(137,234)(138,233)(139,235)(140,236)(141,230)(142,229)(143,231)(144,232);; 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*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(288)!( 1, 9)( 2, 10)( 3, 12)( 4, 11)( 5, 13)( 6, 14)( 7, 16)( 8, 15)( 17, 25)( 18, 26)( 19, 28)( 20, 27)( 21, 29)( 22, 30)( 23, 32)( 24, 31)( 33, 41)( 34, 42)( 35, 44)( 36, 43)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 49,105)( 50,106)( 51,108)( 52,107)( 53,109)( 54,110)( 55,112)( 56,111)( 57, 97)( 58, 98)( 59,100)( 60, 99)( 61,101)( 62,102)( 63,104)( 64,103)( 65,121)( 66,122)( 67,124)( 68,123)( 69,125)( 70,126)( 71,128)( 72,127)( 73,113)( 74,114)( 75,116)( 76,115)( 77,117)( 78,118)( 79,120)( 80,119)( 81,137)( 82,138)( 83,140)( 84,139)( 85,141)( 86,142)( 87,144)( 88,143)( 89,129)( 90,130)( 91,132)( 92,131)( 93,133)( 94,134)( 95,136)( 96,135)(145,153)(146,154)(147,156)(148,155)(149,157)(150,158)(151,160)(152,159)(161,169)(162,170)(163,172)(164,171)(165,173)(166,174)(167,176)(168,175)(177,185)(178,186)(179,188)(180,187)(181,189)(182,190)(183,192)(184,191)(193,249)(194,250)(195,252)(196,251)(197,253)(198,254)(199,256)(200,255)(201,241)(202,242)(203,244)(204,243)(205,245)(206,246)(207,248)(208,247)(209,265)(210,266)(211,268)(212,267)(213,269)(214,270)(215,272)(216,271)(217,257)(218,258)(219,260)(220,259)(221,261)(222,262)(223,264)(224,263)(225,281)(226,282)(227,284)(228,283)(229,285)(230,286)(231,288)(232,287)(233,273)(234,274)(235,276)(236,275)(237,277)(238,278)(239,280)(240,279); s1 := Sym(288)!( 1, 49)( 2, 52)( 3, 51)( 4, 50)( 5, 53)( 6, 56)( 7, 55)( 8, 54)( 9, 61)( 10, 64)( 11, 63)( 12, 62)( 13, 57)( 14, 60)( 15, 59)( 16, 58)( 17, 81)( 18, 84)( 19, 83)( 20, 82)( 21, 85)( 22, 88)( 23, 87)( 24, 86)( 25, 93)( 26, 96)( 27, 95)( 28, 94)( 29, 89)( 30, 92)( 31, 91)( 32, 90)( 33, 65)( 34, 68)( 35, 67)( 36, 66)( 37, 69)( 38, 72)( 39, 71)( 40, 70)( 41, 77)( 42, 80)( 43, 79)( 44, 78)( 45, 73)( 46, 76)( 47, 75)( 48, 74)( 98,100)(102,104)(105,109)(106,112)(107,111)(108,110)(113,129)(114,132)(115,131)(116,130)(117,133)(118,136)(119,135)(120,134)(121,141)(122,144)(123,143)(124,142)(125,137)(126,140)(127,139)(128,138)(145,193)(146,196)(147,195)(148,194)(149,197)(150,200)(151,199)(152,198)(153,205)(154,208)(155,207)(156,206)(157,201)(158,204)(159,203)(160,202)(161,225)(162,228)(163,227)(164,226)(165,229)(166,232)(167,231)(168,230)(169,237)(170,240)(171,239)(172,238)(173,233)(174,236)(175,235)(176,234)(177,209)(178,212)(179,211)(180,210)(181,213)(182,216)(183,215)(184,214)(185,221)(186,224)(187,223)(188,222)(189,217)(190,220)(191,219)(192,218)(242,244)(246,248)(249,253)(250,256)(251,255)(252,254)(257,273)(258,276)(259,275)(260,274)(261,277)(262,280)(263,279)(264,278)(265,285)(266,288)(267,287)(268,286)(269,281)(270,284)(271,283)(272,282); s2 := Sym(288)!( 1,162)( 2,161)( 3,163)( 4,164)( 5,174)( 6,173)( 7,175)( 8,176)( 9,170)( 10,169)( 11,171)( 12,172)( 13,166)( 14,165)( 15,167)( 16,168)( 17,146)( 18,145)( 19,147)( 20,148)( 21,158)( 22,157)( 23,159)( 24,160)( 25,154)( 26,153)( 27,155)( 28,156)( 29,150)( 30,149)( 31,151)( 32,152)( 33,178)( 34,177)( 35,179)( 36,180)( 37,190)( 38,189)( 39,191)( 40,192)( 41,186)( 42,185)( 43,187)( 44,188)( 45,182)( 46,181)( 47,183)( 48,184)( 49,258)( 50,257)( 51,259)( 52,260)( 53,270)( 54,269)( 55,271)( 56,272)( 57,266)( 58,265)( 59,267)( 60,268)( 61,262)( 62,261)( 63,263)( 64,264)( 65,242)( 66,241)( 67,243)( 68,244)( 69,254)( 70,253)( 71,255)( 72,256)( 73,250)( 74,249)( 75,251)( 76,252)( 77,246)( 78,245)( 79,247)( 80,248)( 81,274)( 82,273)( 83,275)( 84,276)( 85,286)( 86,285)( 87,287)( 88,288)( 89,282)( 90,281)( 91,283)( 92,284)( 93,278)( 94,277)( 95,279)( 96,280)( 97,210)( 98,209)( 99,211)(100,212)(101,222)(102,221)(103,223)(104,224)(105,218)(106,217)(107,219)(108,220)(109,214)(110,213)(111,215)(112,216)(113,194)(114,193)(115,195)(116,196)(117,206)(118,205)(119,207)(120,208)(121,202)(122,201)(123,203)(124,204)(125,198)(126,197)(127,199)(128,200)(129,226)(130,225)(131,227)(132,228)(133,238)(134,237)(135,239)(136,240)(137,234)(138,233)(139,235)(140,236)(141,230)(142,229)(143,231)(144,232); 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*s2*s1*s0*s1*s2*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*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 >;
References
None.
to this polytope.