Overview
- Group
- SmallGroup(1152,156074)
- Rank
- 3
- Schläfli Type
- {24,6}
- Vertices, edges, …
- 96, 288, 24
- Order of s0s1s2
- 24
- Order of s0s1s2s1
- 6
- 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
36-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)^2*(s2*s1*s0)^2*(s1*s2)^2> of order 2
12 facets
- 12 of {24}*48
48 vertex figures
- 48 of {6}*12
P/N, where N=<(s0*s1)^2*(s2*s1*s0)^2*s2*s1> of order 2
12 facets
- 12 of {24}*48
48 vertex figures
- 48 of {6}*12
P/N, where N=<s0*s1*s0*s2*(s1*s0)^2*s2*s1> of order 2
12 facets
- 12 of {24}*48
48 vertex figures
- 48 of {6}*12
P/N, where N=<s0*s1*s0*s2*(s1*s0)^2*s2*s1, s0*s1*s0*(s2*s1)^2*(s0*s1)^2*s2> of order 4
6 facets
- 6 of {24}*48
24 vertex figures
- 24 of {6}*12
P/N, where N=<s0*s1*s0*(s2*s1)^2*(s0*s1)^2*s2, s0*s2*s1*s0*(s2*s1)^2*(s0*s1)^2> of order 4
6 facets
- 6 of {24}*48
24 vertex figures
- 24 of {6}*12
Representations
Permutation Representation (GAP)
s0 := ( 3, 4)( 7, 8)( 11, 12)( 13, 25)( 14, 26)( 15, 28)( 16, 27)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 33)( 22, 34)( 23, 36)( 24, 35)( 39, 40)( 43, 44)( 47, 48)( 49, 61)( 50, 62)( 51, 64)( 52, 63)( 53, 65)( 54, 66)( 55, 68)( 56, 67)( 57, 69)( 58, 70)( 59, 72)( 60, 71)( 73,109)( 74,110)( 75,112)( 76,111)( 77,113)( 78,114)( 79,116)( 80,115)( 81,117)( 82,118)( 83,120)( 84,119)( 85,133)( 86,134)( 87,136)( 88,135)( 89,137)( 90,138)( 91,140)( 92,139)( 93,141)( 94,142)( 95,144)( 96,143)( 97,121)( 98,122)( 99,124)(100,123)(101,125)(102,126)(103,128)(104,127)(105,129)(106,130)(107,132)(108,131)(145,217)(146,218)(147,220)(148,219)(149,221)(150,222)(151,224)(152,223)(153,225)(154,226)(155,228)(156,227)(157,241)(158,242)(159,244)(160,243)(161,245)(162,246)(163,248)(164,247)(165,249)(166,250)(167,252)(168,251)(169,229)(170,230)(171,232)(172,231)(173,233)(174,234)(175,236)(176,235)(177,237)(178,238)(179,240)(180,239)(181,253)(182,254)(183,256)(184,255)(185,257)(186,258)(187,260)(188,259)(189,261)(190,262)(191,264)(192,263)(193,277)(194,278)(195,280)(196,279)(197,281)(198,282)(199,284)(200,283)(201,285)(202,286)(203,288)(204,287)(205,265)(206,266)(207,268)(208,267)(209,269)(210,270)(211,272)(212,271)(213,273)(214,274)(215,276)(216,275);; s1 := ( 1,157)( 2,160)( 3,159)( 4,158)( 5,165)( 6,168)( 7,167)( 8,166)( 9,161)( 10,164)( 11,163)( 12,162)( 13,145)( 14,148)( 15,147)( 16,146)( 17,153)( 18,156)( 19,155)( 20,154)( 21,149)( 22,152)( 23,151)( 24,150)( 25,169)( 26,172)( 27,171)( 28,170)( 29,177)( 30,180)( 31,179)( 32,178)( 33,173)( 34,176)( 35,175)( 36,174)( 37,193)( 38,196)( 39,195)( 40,194)( 41,201)( 42,204)( 43,203)( 44,202)( 45,197)( 46,200)( 47,199)( 48,198)( 49,181)( 50,184)( 51,183)( 52,182)( 53,189)( 54,192)( 55,191)( 56,190)( 57,185)( 58,188)( 59,187)( 60,186)( 61,205)( 62,208)( 63,207)( 64,206)( 65,213)( 66,216)( 67,215)( 68,214)( 69,209)( 70,212)( 71,211)( 72,210)( 73,265)( 74,268)( 75,267)( 76,266)( 77,273)( 78,276)( 79,275)( 80,274)( 81,269)( 82,272)( 83,271)( 84,270)( 85,253)( 86,256)( 87,255)( 88,254)( 89,261)( 90,264)( 91,263)( 92,262)( 93,257)( 94,260)( 95,259)( 96,258)( 97,277)( 98,280)( 99,279)(100,278)(101,285)(102,288)(103,287)(104,286)(105,281)(106,284)(107,283)(108,282)(109,229)(110,232)(111,231)(112,230)(113,237)(114,240)(115,239)(116,238)(117,233)(118,236)(119,235)(120,234)(121,217)(122,220)(123,219)(124,218)(125,225)(126,228)(127,227)(128,226)(129,221)(130,224)(131,223)(132,222)(133,241)(134,244)(135,243)(136,242)(137,249)(138,252)(139,251)(140,250)(141,245)(142,248)(143,247)(144,246);; s2 := ( 1, 6)( 2, 5)( 3, 7)( 4, 8)( 9, 10)( 13, 30)( 14, 29)( 15, 31)( 16, 32)( 17, 26)( 18, 25)( 19, 27)( 20, 28)( 21, 34)( 22, 33)( 23, 35)( 24, 36)( 37, 42)( 38, 41)( 39, 43)( 40, 44)( 45, 46)( 49, 66)( 50, 65)( 51, 67)( 52, 68)( 53, 62)( 54, 61)( 55, 63)( 56, 64)( 57, 70)( 58, 69)( 59, 71)( 60, 72)( 73, 78)( 74, 77)( 75, 79)( 76, 80)( 81, 82)( 85,102)( 86,101)( 87,103)( 88,104)( 89, 98)( 90, 97)( 91, 99)( 92,100)( 93,106)( 94,105)( 95,107)( 96,108)(109,114)(110,113)(111,115)(112,116)(117,118)(121,138)(122,137)(123,139)(124,140)(125,134)(126,133)(127,135)(128,136)(129,142)(130,141)(131,143)(132,144)(145,150)(146,149)(147,151)(148,152)(153,154)(157,174)(158,173)(159,175)(160,176)(161,170)(162,169)(163,171)(164,172)(165,178)(166,177)(167,179)(168,180)(181,186)(182,185)(183,187)(184,188)(189,190)(193,210)(194,209)(195,211)(196,212)(197,206)(198,205)(199,207)(200,208)(201,214)(202,213)(203,215)(204,216)(217,222)(218,221)(219,223)(220,224)(225,226)(229,246)(230,245)(231,247)(232,248)(233,242)(234,241)(235,243)(236,244)(237,250)(238,249)(239,251)(240,252)(253,258)(254,257)(255,259)(256,260)(261,262)(265,282)(266,281)(267,283)(268,284)(269,278)(270,277)(271,279)(272,280)(273,286)(274,285)(275,287)(276,288);; 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, 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*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(288)!( 3, 4)( 7, 8)( 11, 12)( 13, 25)( 14, 26)( 15, 28)( 16, 27)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 33)( 22, 34)( 23, 36)( 24, 35)( 39, 40)( 43, 44)( 47, 48)( 49, 61)( 50, 62)( 51, 64)( 52, 63)( 53, 65)( 54, 66)( 55, 68)( 56, 67)( 57, 69)( 58, 70)( 59, 72)( 60, 71)( 73,109)( 74,110)( 75,112)( 76,111)( 77,113)( 78,114)( 79,116)( 80,115)( 81,117)( 82,118)( 83,120)( 84,119)( 85,133)( 86,134)( 87,136)( 88,135)( 89,137)( 90,138)( 91,140)( 92,139)( 93,141)( 94,142)( 95,144)( 96,143)( 97,121)( 98,122)( 99,124)(100,123)(101,125)(102,126)(103,128)(104,127)(105,129)(106,130)(107,132)(108,131)(145,217)(146,218)(147,220)(148,219)(149,221)(150,222)(151,224)(152,223)(153,225)(154,226)(155,228)(156,227)(157,241)(158,242)(159,244)(160,243)(161,245)(162,246)(163,248)(164,247)(165,249)(166,250)(167,252)(168,251)(169,229)(170,230)(171,232)(172,231)(173,233)(174,234)(175,236)(176,235)(177,237)(178,238)(179,240)(180,239)(181,253)(182,254)(183,256)(184,255)(185,257)(186,258)(187,260)(188,259)(189,261)(190,262)(191,264)(192,263)(193,277)(194,278)(195,280)(196,279)(197,281)(198,282)(199,284)(200,283)(201,285)(202,286)(203,288)(204,287)(205,265)(206,266)(207,268)(208,267)(209,269)(210,270)(211,272)(212,271)(213,273)(214,274)(215,276)(216,275); s1 := Sym(288)!( 1,157)( 2,160)( 3,159)( 4,158)( 5,165)( 6,168)( 7,167)( 8,166)( 9,161)( 10,164)( 11,163)( 12,162)( 13,145)( 14,148)( 15,147)( 16,146)( 17,153)( 18,156)( 19,155)( 20,154)( 21,149)( 22,152)( 23,151)( 24,150)( 25,169)( 26,172)( 27,171)( 28,170)( 29,177)( 30,180)( 31,179)( 32,178)( 33,173)( 34,176)( 35,175)( 36,174)( 37,193)( 38,196)( 39,195)( 40,194)( 41,201)( 42,204)( 43,203)( 44,202)( 45,197)( 46,200)( 47,199)( 48,198)( 49,181)( 50,184)( 51,183)( 52,182)( 53,189)( 54,192)( 55,191)( 56,190)( 57,185)( 58,188)( 59,187)( 60,186)( 61,205)( 62,208)( 63,207)( 64,206)( 65,213)( 66,216)( 67,215)( 68,214)( 69,209)( 70,212)( 71,211)( 72,210)( 73,265)( 74,268)( 75,267)( 76,266)( 77,273)( 78,276)( 79,275)( 80,274)( 81,269)( 82,272)( 83,271)( 84,270)( 85,253)( 86,256)( 87,255)( 88,254)( 89,261)( 90,264)( 91,263)( 92,262)( 93,257)( 94,260)( 95,259)( 96,258)( 97,277)( 98,280)( 99,279)(100,278)(101,285)(102,288)(103,287)(104,286)(105,281)(106,284)(107,283)(108,282)(109,229)(110,232)(111,231)(112,230)(113,237)(114,240)(115,239)(116,238)(117,233)(118,236)(119,235)(120,234)(121,217)(122,220)(123,219)(124,218)(125,225)(126,228)(127,227)(128,226)(129,221)(130,224)(131,223)(132,222)(133,241)(134,244)(135,243)(136,242)(137,249)(138,252)(139,251)(140,250)(141,245)(142,248)(143,247)(144,246); s2 := Sym(288)!( 1, 6)( 2, 5)( 3, 7)( 4, 8)( 9, 10)( 13, 30)( 14, 29)( 15, 31)( 16, 32)( 17, 26)( 18, 25)( 19, 27)( 20, 28)( 21, 34)( 22, 33)( 23, 35)( 24, 36)( 37, 42)( 38, 41)( 39, 43)( 40, 44)( 45, 46)( 49, 66)( 50, 65)( 51, 67)( 52, 68)( 53, 62)( 54, 61)( 55, 63)( 56, 64)( 57, 70)( 58, 69)( 59, 71)( 60, 72)( 73, 78)( 74, 77)( 75, 79)( 76, 80)( 81, 82)( 85,102)( 86,101)( 87,103)( 88,104)( 89, 98)( 90, 97)( 91, 99)( 92,100)( 93,106)( 94,105)( 95,107)( 96,108)(109,114)(110,113)(111,115)(112,116)(117,118)(121,138)(122,137)(123,139)(124,140)(125,134)(126,133)(127,135)(128,136)(129,142)(130,141)(131,143)(132,144)(145,150)(146,149)(147,151)(148,152)(153,154)(157,174)(158,173)(159,175)(160,176)(161,170)(162,169)(163,171)(164,172)(165,178)(166,177)(167,179)(168,180)(181,186)(182,185)(183,187)(184,188)(189,190)(193,210)(194,209)(195,211)(196,212)(197,206)(198,205)(199,207)(200,208)(201,214)(202,213)(203,215)(204,216)(217,222)(218,221)(219,223)(220,224)(225,226)(229,246)(230,245)(231,247)(232,248)(233,242)(234,241)(235,243)(236,244)(237,250)(238,249)(239,251)(240,252)(253,258)(254,257)(255,259)(256,260)(261,262)(265,282)(266,281)(267,283)(268,284)(269,278)(270,277)(271,279)(272,280)(273,286)(274,285)(275,287)(276,288); 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, 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*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1 >;
References
None.
to this polytope.