Overview
- Group
- SmallGroup(1152,155849)
- Rank
- 3
- Schläfli Type
- {6,24}
- Vertices, edges, …
- 24, 288, 96
- 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
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
8-fold
12-fold
16-fold
24-fold
32-fold
48-fold
72-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*s2*s1*s0*(s2*s1)^2*(s0*s2*s1)^2*s2> of order 2
48 facets
- 48 of {6}*12
12 vertex figures
- 12 of {24}*48
Representations
Permutation Representation (GAP)
s0 := ( 3, 4)( 5, 7)( 6, 8)( 11, 12)( 13, 15)( 14, 16)( 19, 20)( 21, 23)( 22, 24)( 25, 49)( 26, 50)( 27, 52)( 28, 51)( 29, 55)( 30, 56)( 31, 53)( 32, 54)( 33, 57)( 34, 58)( 35, 60)( 36, 59)( 37, 63)( 38, 64)( 39, 61)( 40, 62)( 41, 65)( 42, 66)( 43, 68)( 44, 67)( 45, 71)( 46, 72)( 47, 69)( 48, 70)( 75, 76)( 77, 79)( 78, 80)( 83, 84)( 85, 87)( 86, 88)( 91, 92)( 93, 95)( 94, 96)( 97,121)( 98,122)( 99,124)(100,123)(101,127)(102,128)(103,125)(104,126)(105,129)(106,130)(107,132)(108,131)(109,135)(110,136)(111,133)(112,134)(113,137)(114,138)(115,140)(116,139)(117,143)(118,144)(119,141)(120,142)(145,146)(149,152)(150,151)(153,154)(157,160)(158,159)(161,162)(165,168)(166,167)(169,194)(170,193)(171,195)(172,196)(173,200)(174,199)(175,198)(176,197)(177,202)(178,201)(179,203)(180,204)(181,208)(182,207)(183,206)(184,205)(185,210)(186,209)(187,211)(188,212)(189,216)(190,215)(191,214)(192,213)(217,218)(221,224)(222,223)(225,226)(229,232)(230,231)(233,234)(237,240)(238,239)(241,266)(242,265)(243,267)(244,268)(245,272)(246,271)(247,270)(248,269)(249,274)(250,273)(251,275)(252,276)(253,280)(254,279)(255,278)(256,277)(257,282)(258,281)(259,283)(260,284)(261,288)(262,287)(263,286)(264,285);; s1 := ( 1, 25)( 2, 26)( 3, 31)( 4, 32)( 5, 30)( 6, 29)( 7, 27)( 8, 28)( 9, 41)( 10, 42)( 11, 47)( 12, 48)( 13, 46)( 14, 45)( 15, 43)( 16, 44)( 17, 33)( 18, 34)( 19, 39)( 20, 40)( 21, 38)( 22, 37)( 23, 35)( 24, 36)( 51, 55)( 52, 56)( 53, 54)( 57, 65)( 58, 66)( 59, 71)( 60, 72)( 61, 70)( 62, 69)( 63, 67)( 64, 68)( 73, 98)( 74, 97)( 75,104)( 76,103)( 77,101)( 78,102)( 79,100)( 80, 99)( 81,114)( 82,113)( 83,120)( 84,119)( 85,117)( 86,118)( 87,116)( 88,115)( 89,106)( 90,105)( 91,112)( 92,111)( 93,109)( 94,110)( 95,108)( 96,107)(121,122)(123,128)(124,127)(129,138)(130,137)(131,144)(132,143)(133,141)(134,142)(135,140)(136,139)(145,242)(146,241)(147,248)(148,247)(149,245)(150,246)(151,244)(152,243)(153,258)(154,257)(155,264)(156,263)(157,261)(158,262)(159,260)(160,259)(161,250)(162,249)(163,256)(164,255)(165,253)(166,254)(167,252)(168,251)(169,218)(170,217)(171,224)(172,223)(173,221)(174,222)(175,220)(176,219)(177,234)(178,233)(179,240)(180,239)(181,237)(182,238)(183,236)(184,235)(185,226)(186,225)(187,232)(188,231)(189,229)(190,230)(191,228)(192,227)(193,266)(194,265)(195,272)(196,271)(197,269)(198,270)(199,268)(200,267)(201,282)(202,281)(203,288)(204,287)(205,285)(206,286)(207,284)(208,283)(209,274)(210,273)(211,280)(212,279)(213,277)(214,278)(215,276)(216,275);; s2 := ( 1,155)( 2,156)( 3,153)( 4,154)( 5,158)( 6,157)( 7,159)( 8,160)( 9,147)( 10,148)( 11,145)( 12,146)( 13,150)( 14,149)( 15,151)( 16,152)( 17,163)( 18,164)( 19,161)( 20,162)( 21,166)( 22,165)( 23,167)( 24,168)( 25,203)( 26,204)( 27,201)( 28,202)( 29,206)( 30,205)( 31,207)( 32,208)( 33,195)( 34,196)( 35,193)( 36,194)( 37,198)( 38,197)( 39,199)( 40,200)( 41,211)( 42,212)( 43,209)( 44,210)( 45,214)( 46,213)( 47,215)( 48,216)( 49,179)( 50,180)( 51,177)( 52,178)( 53,182)( 54,181)( 55,183)( 56,184)( 57,171)( 58,172)( 59,169)( 60,170)( 61,174)( 62,173)( 63,175)( 64,176)( 65,187)( 66,188)( 67,185)( 68,186)( 69,190)( 70,189)( 71,191)( 72,192)( 73,228)( 74,227)( 75,226)( 76,225)( 77,229)( 78,230)( 79,232)( 80,231)( 81,220)( 82,219)( 83,218)( 84,217)( 85,221)( 86,222)( 87,224)( 88,223)( 89,236)( 90,235)( 91,234)( 92,233)( 93,237)( 94,238)( 95,240)( 96,239)( 97,276)( 98,275)( 99,274)(100,273)(101,277)(102,278)(103,280)(104,279)(105,268)(106,267)(107,266)(108,265)(109,269)(110,270)(111,272)(112,271)(113,284)(114,283)(115,282)(116,281)(117,285)(118,286)(119,288)(120,287)(121,252)(122,251)(123,250)(124,249)(125,253)(126,254)(127,256)(128,255)(129,244)(130,243)(131,242)(132,241)(133,245)(134,246)(135,248)(136,247)(137,260)(138,259)(139,258)(140,257)(141,261)(142,262)(143,264)(144,263);; 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*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(288)!( 3, 4)( 5, 7)( 6, 8)( 11, 12)( 13, 15)( 14, 16)( 19, 20)( 21, 23)( 22, 24)( 25, 49)( 26, 50)( 27, 52)( 28, 51)( 29, 55)( 30, 56)( 31, 53)( 32, 54)( 33, 57)( 34, 58)( 35, 60)( 36, 59)( 37, 63)( 38, 64)( 39, 61)( 40, 62)( 41, 65)( 42, 66)( 43, 68)( 44, 67)( 45, 71)( 46, 72)( 47, 69)( 48, 70)( 75, 76)( 77, 79)( 78, 80)( 83, 84)( 85, 87)( 86, 88)( 91, 92)( 93, 95)( 94, 96)( 97,121)( 98,122)( 99,124)(100,123)(101,127)(102,128)(103,125)(104,126)(105,129)(106,130)(107,132)(108,131)(109,135)(110,136)(111,133)(112,134)(113,137)(114,138)(115,140)(116,139)(117,143)(118,144)(119,141)(120,142)(145,146)(149,152)(150,151)(153,154)(157,160)(158,159)(161,162)(165,168)(166,167)(169,194)(170,193)(171,195)(172,196)(173,200)(174,199)(175,198)(176,197)(177,202)(178,201)(179,203)(180,204)(181,208)(182,207)(183,206)(184,205)(185,210)(186,209)(187,211)(188,212)(189,216)(190,215)(191,214)(192,213)(217,218)(221,224)(222,223)(225,226)(229,232)(230,231)(233,234)(237,240)(238,239)(241,266)(242,265)(243,267)(244,268)(245,272)(246,271)(247,270)(248,269)(249,274)(250,273)(251,275)(252,276)(253,280)(254,279)(255,278)(256,277)(257,282)(258,281)(259,283)(260,284)(261,288)(262,287)(263,286)(264,285); s1 := Sym(288)!( 1, 25)( 2, 26)( 3, 31)( 4, 32)( 5, 30)( 6, 29)( 7, 27)( 8, 28)( 9, 41)( 10, 42)( 11, 47)( 12, 48)( 13, 46)( 14, 45)( 15, 43)( 16, 44)( 17, 33)( 18, 34)( 19, 39)( 20, 40)( 21, 38)( 22, 37)( 23, 35)( 24, 36)( 51, 55)( 52, 56)( 53, 54)( 57, 65)( 58, 66)( 59, 71)( 60, 72)( 61, 70)( 62, 69)( 63, 67)( 64, 68)( 73, 98)( 74, 97)( 75,104)( 76,103)( 77,101)( 78,102)( 79,100)( 80, 99)( 81,114)( 82,113)( 83,120)( 84,119)( 85,117)( 86,118)( 87,116)( 88,115)( 89,106)( 90,105)( 91,112)( 92,111)( 93,109)( 94,110)( 95,108)( 96,107)(121,122)(123,128)(124,127)(129,138)(130,137)(131,144)(132,143)(133,141)(134,142)(135,140)(136,139)(145,242)(146,241)(147,248)(148,247)(149,245)(150,246)(151,244)(152,243)(153,258)(154,257)(155,264)(156,263)(157,261)(158,262)(159,260)(160,259)(161,250)(162,249)(163,256)(164,255)(165,253)(166,254)(167,252)(168,251)(169,218)(170,217)(171,224)(172,223)(173,221)(174,222)(175,220)(176,219)(177,234)(178,233)(179,240)(180,239)(181,237)(182,238)(183,236)(184,235)(185,226)(186,225)(187,232)(188,231)(189,229)(190,230)(191,228)(192,227)(193,266)(194,265)(195,272)(196,271)(197,269)(198,270)(199,268)(200,267)(201,282)(202,281)(203,288)(204,287)(205,285)(206,286)(207,284)(208,283)(209,274)(210,273)(211,280)(212,279)(213,277)(214,278)(215,276)(216,275); s2 := Sym(288)!( 1,155)( 2,156)( 3,153)( 4,154)( 5,158)( 6,157)( 7,159)( 8,160)( 9,147)( 10,148)( 11,145)( 12,146)( 13,150)( 14,149)( 15,151)( 16,152)( 17,163)( 18,164)( 19,161)( 20,162)( 21,166)( 22,165)( 23,167)( 24,168)( 25,203)( 26,204)( 27,201)( 28,202)( 29,206)( 30,205)( 31,207)( 32,208)( 33,195)( 34,196)( 35,193)( 36,194)( 37,198)( 38,197)( 39,199)( 40,200)( 41,211)( 42,212)( 43,209)( 44,210)( 45,214)( 46,213)( 47,215)( 48,216)( 49,179)( 50,180)( 51,177)( 52,178)( 53,182)( 54,181)( 55,183)( 56,184)( 57,171)( 58,172)( 59,169)( 60,170)( 61,174)( 62,173)( 63,175)( 64,176)( 65,187)( 66,188)( 67,185)( 68,186)( 69,190)( 70,189)( 71,191)( 72,192)( 73,228)( 74,227)( 75,226)( 76,225)( 77,229)( 78,230)( 79,232)( 80,231)( 81,220)( 82,219)( 83,218)( 84,217)( 85,221)( 86,222)( 87,224)( 88,223)( 89,236)( 90,235)( 91,234)( 92,233)( 93,237)( 94,238)( 95,240)( 96,239)( 97,276)( 98,275)( 99,274)(100,273)(101,277)(102,278)(103,280)(104,279)(105,268)(106,267)(107,266)(108,265)(109,269)(110,270)(111,272)(112,271)(113,284)(114,283)(115,282)(116,281)(117,285)(118,286)(119,288)(120,287)(121,252)(122,251)(123,250)(124,249)(125,253)(126,254)(127,256)(128,255)(129,244)(130,243)(131,242)(132,241)(133,245)(134,246)(135,248)(136,247)(137,260)(138,259)(139,258)(140,257)(141,261)(142,262)(143,264)(144,263); 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*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*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1 >;
References
None.
to this polytope.