Overview
- Group
- SmallGroup(1152,157640)
- Rank
- 4
- Schläfli Type
- {4,6,6}
- Vertices, edges, …
- 4, 48, 72, 24
- Order of s0s1s2s3
- 12
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
8-fold
12-fold
16-fold
24-fold
36-fold
48-fold
72-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=<s1*s2*s1*s3*(s2*s1)^2*s3*s2> of order 2
12 facets
- 12 of {4,6}*48a
4 vertex figures
- 4 of 2-fold non-regular quotient of {6,6}*288a
P/N, where N=<(s1*s2)^2*(s3*s2*s1)^2*s3*s2> of order 2
12 facets
- 12 of {4,6}*48a
4 vertex figures
- 4 of 2-fold non-regular quotient of {6,6}*288a
P/N, where N=<(s1*s2)^2> of order 3
12 facets
4 vertex figures
- 4 of 3-fold non-regular quotient of {6,6}*288a
P/N, where N=<s1*s2*s1*s3*(s2*s1)^2*s3*s2, (s1*s2)^3*s3*s2*s1*s3*s2*s3> of order 4
6 facets
- 6 of {4,6}*48a
4 vertex figures
- 4 of 4-fold non-regular quotient of {6,6}*288a
Representations
Permutation Representation (GAP)
s0 := ( 1, 73)( 2, 74)( 3, 75)( 4, 76)( 5, 77)( 6, 78)( 7, 79)( 8, 80)( 9, 81)( 10, 82)( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 87)( 16, 88)( 17, 89)( 18, 90)( 19, 91)( 20, 92)( 21, 93)( 22, 94)( 23, 95)( 24, 96)( 25, 97)( 26, 98)( 27, 99)( 28,100)( 29,101)( 30,102)( 31,103)( 32,104)( 33,105)( 34,106)( 35,107)( 36,108)( 37,109)( 38,110)( 39,111)( 40,112)( 41,113)( 42,114)( 43,115)( 44,116)( 45,117)( 46,118)( 47,119)( 48,120)( 49,121)( 50,122)( 51,123)( 52,124)( 53,125)( 54,126)( 55,127)( 56,128)( 57,129)( 58,130)( 59,131)( 60,132)( 61,133)( 62,134)( 63,135)( 64,136)( 65,137)( 66,138)( 67,139)( 68,140)( 69,141)( 70,142)( 71,143)( 72,144)(145,217)(146,218)(147,219)(148,220)(149,221)(150,222)(151,223)(152,224)(153,225)(154,226)(155,227)(156,228)(157,229)(158,230)(159,231)(160,232)(161,233)(162,234)(163,235)(164,236)(165,237)(166,238)(167,239)(168,240)(169,241)(170,242)(171,243)(172,244)(173,245)(174,246)(175,247)(176,248)(177,249)(178,250)(179,251)(180,252)(181,253)(182,254)(183,255)(184,256)(185,257)(186,258)(187,259)(188,260)(189,261)(190,262)(191,263)(192,264)(193,265)(194,266)(195,267)(196,268)(197,269)(198,270)(199,271)(200,272)(201,273)(202,274)(203,275)(204,276)(205,277)(206,278)(207,279)(208,280)(209,281)(210,282)(211,283)(212,284)(213,285)(214,286)(215,287)(216,288);; s1 := ( 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)(147,148)(151,152)(155,156)(157,169)(158,170)(159,172)(160,171)(161,173)(162,174)(163,176)(164,175)(165,177)(166,178)(167,180)(168,179)(183,184)(187,188)(191,192)(193,205)(194,206)(195,208)(196,207)(197,209)(198,210)(199,212)(200,211)(201,213)(202,214)(203,216)(204,215)(217,253)(218,254)(219,256)(220,255)(221,257)(222,258)(223,260)(224,259)(225,261)(226,262)(227,264)(228,263)(229,277)(230,278)(231,280)(232,279)(233,281)(234,282)(235,284)(236,283)(237,285)(238,286)(239,288)(240,287)(241,265)(242,266)(243,268)(244,267)(245,269)(246,270)(247,272)(248,271)(249,273)(250,274)(251,276)(252,275);; s2 := ( 1, 13)( 2, 16)( 3, 15)( 4, 14)( 5, 21)( 6, 24)( 7, 23)( 8, 22)( 9, 17)( 10, 20)( 11, 19)( 12, 18)( 26, 28)( 29, 33)( 30, 36)( 31, 35)( 32, 34)( 37, 49)( 38, 52)( 39, 51)( 40, 50)( 41, 57)( 42, 60)( 43, 59)( 44, 58)( 45, 53)( 46, 56)( 47, 55)( 48, 54)( 62, 64)( 65, 69)( 66, 72)( 67, 71)( 68, 70)( 73, 85)( 74, 88)( 75, 87)( 76, 86)( 77, 93)( 78, 96)( 79, 95)( 80, 94)( 81, 89)( 82, 92)( 83, 91)( 84, 90)( 98,100)(101,105)(102,108)(103,107)(104,106)(109,121)(110,124)(111,123)(112,122)(113,129)(114,132)(115,131)(116,130)(117,125)(118,128)(119,127)(120,126)(134,136)(137,141)(138,144)(139,143)(140,142)(145,157)(146,160)(147,159)(148,158)(149,165)(150,168)(151,167)(152,166)(153,161)(154,164)(155,163)(156,162)(170,172)(173,177)(174,180)(175,179)(176,178)(181,193)(182,196)(183,195)(184,194)(185,201)(186,204)(187,203)(188,202)(189,197)(190,200)(191,199)(192,198)(206,208)(209,213)(210,216)(211,215)(212,214)(217,229)(218,232)(219,231)(220,230)(221,237)(222,240)(223,239)(224,238)(225,233)(226,236)(227,235)(228,234)(242,244)(245,249)(246,252)(247,251)(248,250)(253,265)(254,268)(255,267)(256,266)(257,273)(258,276)(259,275)(260,274)(261,269)(262,272)(263,271)(264,270)(278,280)(281,285)(282,288)(283,287)(284,286);; s3 := ( 1,150)( 2,149)( 3,151)( 4,152)( 5,146)( 6,145)( 7,147)( 8,148)( 9,154)( 10,153)( 11,155)( 12,156)( 13,174)( 14,173)( 15,175)( 16,176)( 17,170)( 18,169)( 19,171)( 20,172)( 21,178)( 22,177)( 23,179)( 24,180)( 25,162)( 26,161)( 27,163)( 28,164)( 29,158)( 30,157)( 31,159)( 32,160)( 33,166)( 34,165)( 35,167)( 36,168)( 37,186)( 38,185)( 39,187)( 40,188)( 41,182)( 42,181)( 43,183)( 44,184)( 45,190)( 46,189)( 47,191)( 48,192)( 49,210)( 50,209)( 51,211)( 52,212)( 53,206)( 54,205)( 55,207)( 56,208)( 57,214)( 58,213)( 59,215)( 60,216)( 61,198)( 62,197)( 63,199)( 64,200)( 65,194)( 66,193)( 67,195)( 68,196)( 69,202)( 70,201)( 71,203)( 72,204)( 73,222)( 74,221)( 75,223)( 76,224)( 77,218)( 78,217)( 79,219)( 80,220)( 81,226)( 82,225)( 83,227)( 84,228)( 85,246)( 86,245)( 87,247)( 88,248)( 89,242)( 90,241)( 91,243)( 92,244)( 93,250)( 94,249)( 95,251)( 96,252)( 97,234)( 98,233)( 99,235)(100,236)(101,230)(102,229)(103,231)(104,232)(105,238)(106,237)(107,239)(108,240)(109,258)(110,257)(111,259)(112,260)(113,254)(114,253)(115,255)(116,256)(117,262)(118,261)(119,263)(120,264)(121,282)(122,281)(123,283)(124,284)(125,278)(126,277)(127,279)(128,280)(129,286)(130,285)(131,287)(132,288)(133,270)(134,269)(135,271)(136,272)(137,266)(138,265)(139,267)(140,268)(141,274)(142,273)(143,275)(144,276);; 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, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(288)!( 1, 73)( 2, 74)( 3, 75)( 4, 76)( 5, 77)( 6, 78)( 7, 79)( 8, 80)( 9, 81)( 10, 82)( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 87)( 16, 88)( 17, 89)( 18, 90)( 19, 91)( 20, 92)( 21, 93)( 22, 94)( 23, 95)( 24, 96)( 25, 97)( 26, 98)( 27, 99)( 28,100)( 29,101)( 30,102)( 31,103)( 32,104)( 33,105)( 34,106)( 35,107)( 36,108)( 37,109)( 38,110)( 39,111)( 40,112)( 41,113)( 42,114)( 43,115)( 44,116)( 45,117)( 46,118)( 47,119)( 48,120)( 49,121)( 50,122)( 51,123)( 52,124)( 53,125)( 54,126)( 55,127)( 56,128)( 57,129)( 58,130)( 59,131)( 60,132)( 61,133)( 62,134)( 63,135)( 64,136)( 65,137)( 66,138)( 67,139)( 68,140)( 69,141)( 70,142)( 71,143)( 72,144)(145,217)(146,218)(147,219)(148,220)(149,221)(150,222)(151,223)(152,224)(153,225)(154,226)(155,227)(156,228)(157,229)(158,230)(159,231)(160,232)(161,233)(162,234)(163,235)(164,236)(165,237)(166,238)(167,239)(168,240)(169,241)(170,242)(171,243)(172,244)(173,245)(174,246)(175,247)(176,248)(177,249)(178,250)(179,251)(180,252)(181,253)(182,254)(183,255)(184,256)(185,257)(186,258)(187,259)(188,260)(189,261)(190,262)(191,263)(192,264)(193,265)(194,266)(195,267)(196,268)(197,269)(198,270)(199,271)(200,272)(201,273)(202,274)(203,275)(204,276)(205,277)(206,278)(207,279)(208,280)(209,281)(210,282)(211,283)(212,284)(213,285)(214,286)(215,287)(216,288); s1 := 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)(147,148)(151,152)(155,156)(157,169)(158,170)(159,172)(160,171)(161,173)(162,174)(163,176)(164,175)(165,177)(166,178)(167,180)(168,179)(183,184)(187,188)(191,192)(193,205)(194,206)(195,208)(196,207)(197,209)(198,210)(199,212)(200,211)(201,213)(202,214)(203,216)(204,215)(217,253)(218,254)(219,256)(220,255)(221,257)(222,258)(223,260)(224,259)(225,261)(226,262)(227,264)(228,263)(229,277)(230,278)(231,280)(232,279)(233,281)(234,282)(235,284)(236,283)(237,285)(238,286)(239,288)(240,287)(241,265)(242,266)(243,268)(244,267)(245,269)(246,270)(247,272)(248,271)(249,273)(250,274)(251,276)(252,275); s2 := Sym(288)!( 1, 13)( 2, 16)( 3, 15)( 4, 14)( 5, 21)( 6, 24)( 7, 23)( 8, 22)( 9, 17)( 10, 20)( 11, 19)( 12, 18)( 26, 28)( 29, 33)( 30, 36)( 31, 35)( 32, 34)( 37, 49)( 38, 52)( 39, 51)( 40, 50)( 41, 57)( 42, 60)( 43, 59)( 44, 58)( 45, 53)( 46, 56)( 47, 55)( 48, 54)( 62, 64)( 65, 69)( 66, 72)( 67, 71)( 68, 70)( 73, 85)( 74, 88)( 75, 87)( 76, 86)( 77, 93)( 78, 96)( 79, 95)( 80, 94)( 81, 89)( 82, 92)( 83, 91)( 84, 90)( 98,100)(101,105)(102,108)(103,107)(104,106)(109,121)(110,124)(111,123)(112,122)(113,129)(114,132)(115,131)(116,130)(117,125)(118,128)(119,127)(120,126)(134,136)(137,141)(138,144)(139,143)(140,142)(145,157)(146,160)(147,159)(148,158)(149,165)(150,168)(151,167)(152,166)(153,161)(154,164)(155,163)(156,162)(170,172)(173,177)(174,180)(175,179)(176,178)(181,193)(182,196)(183,195)(184,194)(185,201)(186,204)(187,203)(188,202)(189,197)(190,200)(191,199)(192,198)(206,208)(209,213)(210,216)(211,215)(212,214)(217,229)(218,232)(219,231)(220,230)(221,237)(222,240)(223,239)(224,238)(225,233)(226,236)(227,235)(228,234)(242,244)(245,249)(246,252)(247,251)(248,250)(253,265)(254,268)(255,267)(256,266)(257,273)(258,276)(259,275)(260,274)(261,269)(262,272)(263,271)(264,270)(278,280)(281,285)(282,288)(283,287)(284,286); s3 := Sym(288)!( 1,150)( 2,149)( 3,151)( 4,152)( 5,146)( 6,145)( 7,147)( 8,148)( 9,154)( 10,153)( 11,155)( 12,156)( 13,174)( 14,173)( 15,175)( 16,176)( 17,170)( 18,169)( 19,171)( 20,172)( 21,178)( 22,177)( 23,179)( 24,180)( 25,162)( 26,161)( 27,163)( 28,164)( 29,158)( 30,157)( 31,159)( 32,160)( 33,166)( 34,165)( 35,167)( 36,168)( 37,186)( 38,185)( 39,187)( 40,188)( 41,182)( 42,181)( 43,183)( 44,184)( 45,190)( 46,189)( 47,191)( 48,192)( 49,210)( 50,209)( 51,211)( 52,212)( 53,206)( 54,205)( 55,207)( 56,208)( 57,214)( 58,213)( 59,215)( 60,216)( 61,198)( 62,197)( 63,199)( 64,200)( 65,194)( 66,193)( 67,195)( 68,196)( 69,202)( 70,201)( 71,203)( 72,204)( 73,222)( 74,221)( 75,223)( 76,224)( 77,218)( 78,217)( 79,219)( 80,220)( 81,226)( 82,225)( 83,227)( 84,228)( 85,246)( 86,245)( 87,247)( 88,248)( 89,242)( 90,241)( 91,243)( 92,244)( 93,250)( 94,249)( 95,251)( 96,252)( 97,234)( 98,233)( 99,235)(100,236)(101,230)(102,229)(103,231)(104,232)(105,238)(106,237)(107,239)(108,240)(109,258)(110,257)(111,259)(112,260)(113,254)(114,253)(115,255)(116,256)(117,262)(118,261)(119,263)(120,264)(121,282)(122,281)(123,283)(124,284)(125,278)(126,277)(127,279)(128,280)(129,286)(130,285)(131,287)(132,288)(133,270)(134,269)(135,271)(136,272)(137,266)(138,265)(139,267)(140,268)(141,274)(142,273)(143,275)(144,276); poly := sub<Sym(288)|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, s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2 >;
References
None.
to this polytope.