Overview
- Group
- SmallGroup(1152,98809)
- Rank
- 4
- Schläfli Type
- {8,12,2}
- Vertices, edges, …
- 24, 144, 36, 2
- Order of s0s1s2s3
- 8
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
4-fold
8-fold
9-fold
18-fold
36-fold
72-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := ( 4, 7)( 5, 8)( 6, 9)( 13, 16)( 14, 17)( 15, 18)( 19, 28)( 20, 29)( 21, 30)( 22, 34)( 23, 35)( 24, 36)( 25, 31)( 26, 32)( 27, 33)( 37, 46)( 38, 47)( 39, 48)( 40, 52)( 41, 53)( 42, 54)( 43, 49)( 44, 50)( 45, 51)( 58, 61)( 59, 62)( 60, 63)( 67, 70)( 68, 71)( 69, 72)( 76, 79)( 77, 80)( 78, 81)( 85, 88)( 86, 89)( 87, 90)( 91,100)( 92,101)( 93,102)( 94,106)( 95,107)( 96,108)( 97,103)( 98,104)( 99,105)(109,118)(110,119)(111,120)(112,124)(113,125)(114,126)(115,121)(116,122)(117,123)(130,133)(131,134)(132,135)(139,142)(140,143)(141,144)(145,181)(146,182)(147,183)(148,187)(149,188)(150,189)(151,184)(152,185)(153,186)(154,190)(155,191)(156,192)(157,196)(158,197)(159,198)(160,193)(161,194)(162,195)(163,208)(164,209)(165,210)(166,214)(167,215)(168,216)(169,211)(170,212)(171,213)(172,199)(173,200)(174,201)(175,205)(176,206)(177,207)(178,202)(179,203)(180,204)(217,262)(218,263)(219,264)(220,268)(221,269)(222,270)(223,265)(224,266)(225,267)(226,253)(227,254)(228,255)(229,259)(230,260)(231,261)(232,256)(233,257)(234,258)(235,271)(236,272)(237,273)(238,277)(239,278)(240,279)(241,274)(242,275)(243,276)(244,280)(245,281)(246,282)(247,286)(248,287)(249,288)(250,283)(251,284)(252,285);; s1 := ( 1,145)( 2,148)( 3,151)( 4,146)( 5,149)( 6,152)( 7,147)( 8,150)( 9,153)( 10,154)( 11,157)( 12,160)( 13,155)( 14,158)( 15,161)( 16,156)( 17,159)( 18,162)( 19,163)( 20,166)( 21,169)( 22,164)( 23,167)( 24,170)( 25,165)( 26,168)( 27,171)( 28,172)( 29,175)( 30,178)( 31,173)( 32,176)( 33,179)( 34,174)( 35,177)( 36,180)( 37,190)( 38,193)( 39,196)( 40,191)( 41,194)( 42,197)( 43,192)( 44,195)( 45,198)( 46,181)( 47,184)( 48,187)( 49,182)( 50,185)( 51,188)( 52,183)( 53,186)( 54,189)( 55,208)( 56,211)( 57,214)( 58,209)( 59,212)( 60,215)( 61,210)( 62,213)( 63,216)( 64,199)( 65,202)( 66,205)( 67,200)( 68,203)( 69,206)( 70,201)( 71,204)( 72,207)( 73,235)( 74,238)( 75,241)( 76,236)( 77,239)( 78,242)( 79,237)( 80,240)( 81,243)( 82,244)( 83,247)( 84,250)( 85,245)( 86,248)( 87,251)( 88,246)( 89,249)( 90,252)( 91,217)( 92,220)( 93,223)( 94,218)( 95,221)( 96,224)( 97,219)( 98,222)( 99,225)(100,226)(101,229)(102,232)(103,227)(104,230)(105,233)(106,228)(107,231)(108,234)(109,280)(110,283)(111,286)(112,281)(113,284)(114,287)(115,282)(116,285)(117,288)(118,271)(119,274)(120,277)(121,272)(122,275)(123,278)(124,273)(125,276)(126,279)(127,262)(128,265)(129,268)(130,263)(131,266)(132,269)(133,264)(134,267)(135,270)(136,253)(137,256)(138,259)(139,254)(140,257)(141,260)(142,255)(143,258)(144,261);; s2 := ( 1,128)( 2,127)( 3,129)( 4,134)( 5,133)( 6,135)( 7,131)( 8,130)( 9,132)( 10,137)( 11,136)( 12,138)( 13,143)( 14,142)( 15,144)( 16,140)( 17,139)( 18,141)( 19,110)( 20,109)( 21,111)( 22,116)( 23,115)( 24,117)( 25,113)( 26,112)( 27,114)( 28,119)( 29,118)( 30,120)( 31,125)( 32,124)( 33,126)( 34,122)( 35,121)( 36,123)( 37, 92)( 38, 91)( 39, 93)( 40, 98)( 41, 97)( 42, 99)( 43, 95)( 44, 94)( 45, 96)( 46,101)( 47,100)( 48,102)( 49,107)( 50,106)( 51,108)( 52,104)( 53,103)( 54,105)( 55, 74)( 56, 73)( 57, 75)( 58, 80)( 59, 79)( 60, 81)( 61, 77)( 62, 76)( 63, 78)( 64, 83)( 65, 82)( 66, 84)( 67, 89)( 68, 88)( 69, 90)( 70, 86)( 71, 85)( 72, 87)(145,272)(146,271)(147,273)(148,278)(149,277)(150,279)(151,275)(152,274)(153,276)(154,281)(155,280)(156,282)(157,287)(158,286)(159,288)(160,284)(161,283)(162,285)(163,254)(164,253)(165,255)(166,260)(167,259)(168,261)(169,257)(170,256)(171,258)(172,263)(173,262)(174,264)(175,269)(176,268)(177,270)(178,266)(179,265)(180,267)(181,236)(182,235)(183,237)(184,242)(185,241)(186,243)(187,239)(188,238)(189,240)(190,245)(191,244)(192,246)(193,251)(194,250)(195,252)(196,248)(197,247)(198,249)(199,218)(200,217)(201,219)(202,224)(203,223)(204,225)(205,221)(206,220)(207,222)(208,227)(209,226)(210,228)(211,233)(212,232)(213,234)(214,230)(215,229)(216,231);; s3 := (289,290);; poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(290)!( 4, 7)( 5, 8)( 6, 9)( 13, 16)( 14, 17)( 15, 18)( 19, 28)( 20, 29)( 21, 30)( 22, 34)( 23, 35)( 24, 36)( 25, 31)( 26, 32)( 27, 33)( 37, 46)( 38, 47)( 39, 48)( 40, 52)( 41, 53)( 42, 54)( 43, 49)( 44, 50)( 45, 51)( 58, 61)( 59, 62)( 60, 63)( 67, 70)( 68, 71)( 69, 72)( 76, 79)( 77, 80)( 78, 81)( 85, 88)( 86, 89)( 87, 90)( 91,100)( 92,101)( 93,102)( 94,106)( 95,107)( 96,108)( 97,103)( 98,104)( 99,105)(109,118)(110,119)(111,120)(112,124)(113,125)(114,126)(115,121)(116,122)(117,123)(130,133)(131,134)(132,135)(139,142)(140,143)(141,144)(145,181)(146,182)(147,183)(148,187)(149,188)(150,189)(151,184)(152,185)(153,186)(154,190)(155,191)(156,192)(157,196)(158,197)(159,198)(160,193)(161,194)(162,195)(163,208)(164,209)(165,210)(166,214)(167,215)(168,216)(169,211)(170,212)(171,213)(172,199)(173,200)(174,201)(175,205)(176,206)(177,207)(178,202)(179,203)(180,204)(217,262)(218,263)(219,264)(220,268)(221,269)(222,270)(223,265)(224,266)(225,267)(226,253)(227,254)(228,255)(229,259)(230,260)(231,261)(232,256)(233,257)(234,258)(235,271)(236,272)(237,273)(238,277)(239,278)(240,279)(241,274)(242,275)(243,276)(244,280)(245,281)(246,282)(247,286)(248,287)(249,288)(250,283)(251,284)(252,285); s1 := Sym(290)!( 1,145)( 2,148)( 3,151)( 4,146)( 5,149)( 6,152)( 7,147)( 8,150)( 9,153)( 10,154)( 11,157)( 12,160)( 13,155)( 14,158)( 15,161)( 16,156)( 17,159)( 18,162)( 19,163)( 20,166)( 21,169)( 22,164)( 23,167)( 24,170)( 25,165)( 26,168)( 27,171)( 28,172)( 29,175)( 30,178)( 31,173)( 32,176)( 33,179)( 34,174)( 35,177)( 36,180)( 37,190)( 38,193)( 39,196)( 40,191)( 41,194)( 42,197)( 43,192)( 44,195)( 45,198)( 46,181)( 47,184)( 48,187)( 49,182)( 50,185)( 51,188)( 52,183)( 53,186)( 54,189)( 55,208)( 56,211)( 57,214)( 58,209)( 59,212)( 60,215)( 61,210)( 62,213)( 63,216)( 64,199)( 65,202)( 66,205)( 67,200)( 68,203)( 69,206)( 70,201)( 71,204)( 72,207)( 73,235)( 74,238)( 75,241)( 76,236)( 77,239)( 78,242)( 79,237)( 80,240)( 81,243)( 82,244)( 83,247)( 84,250)( 85,245)( 86,248)( 87,251)( 88,246)( 89,249)( 90,252)( 91,217)( 92,220)( 93,223)( 94,218)( 95,221)( 96,224)( 97,219)( 98,222)( 99,225)(100,226)(101,229)(102,232)(103,227)(104,230)(105,233)(106,228)(107,231)(108,234)(109,280)(110,283)(111,286)(112,281)(113,284)(114,287)(115,282)(116,285)(117,288)(118,271)(119,274)(120,277)(121,272)(122,275)(123,278)(124,273)(125,276)(126,279)(127,262)(128,265)(129,268)(130,263)(131,266)(132,269)(133,264)(134,267)(135,270)(136,253)(137,256)(138,259)(139,254)(140,257)(141,260)(142,255)(143,258)(144,261); s2 := Sym(290)!( 1,128)( 2,127)( 3,129)( 4,134)( 5,133)( 6,135)( 7,131)( 8,130)( 9,132)( 10,137)( 11,136)( 12,138)( 13,143)( 14,142)( 15,144)( 16,140)( 17,139)( 18,141)( 19,110)( 20,109)( 21,111)( 22,116)( 23,115)( 24,117)( 25,113)( 26,112)( 27,114)( 28,119)( 29,118)( 30,120)( 31,125)( 32,124)( 33,126)( 34,122)( 35,121)( 36,123)( 37, 92)( 38, 91)( 39, 93)( 40, 98)( 41, 97)( 42, 99)( 43, 95)( 44, 94)( 45, 96)( 46,101)( 47,100)( 48,102)( 49,107)( 50,106)( 51,108)( 52,104)( 53,103)( 54,105)( 55, 74)( 56, 73)( 57, 75)( 58, 80)( 59, 79)( 60, 81)( 61, 77)( 62, 76)( 63, 78)( 64, 83)( 65, 82)( 66, 84)( 67, 89)( 68, 88)( 69, 90)( 70, 86)( 71, 85)( 72, 87)(145,272)(146,271)(147,273)(148,278)(149,277)(150,279)(151,275)(152,274)(153,276)(154,281)(155,280)(156,282)(157,287)(158,286)(159,288)(160,284)(161,283)(162,285)(163,254)(164,253)(165,255)(166,260)(167,259)(168,261)(169,257)(170,256)(171,258)(172,263)(173,262)(174,264)(175,269)(176,268)(177,270)(178,266)(179,265)(180,267)(181,236)(182,235)(183,237)(184,242)(185,241)(186,243)(187,239)(188,238)(189,240)(190,245)(191,244)(192,246)(193,251)(194,250)(195,252)(196,248)(197,247)(198,249)(199,218)(200,217)(201,219)(202,224)(203,223)(204,225)(205,221)(206,220)(207,222)(208,227)(209,226)(210,228)(211,233)(212,232)(213,234)(214,230)(215,229)(216,231); s3 := Sym(290)!(289,290); poly := sub<Sym(290)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2 >;