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# Polytope of Type {4,24,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,24,6}*1152j
if this polytope has a name.
Group : SmallGroup(1152,155800)
Rank : 4
Schlafli Type : {4,24,6}
Number of vertices, edges, etc : 4, 48, 72, 6
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,12,6}*576e
3-fold quotients : {4,24,2}*384d
4-fold quotients : {4,6,6}*288e
6-fold quotients : {4,12,2}*192b
8-fold quotients : {4,3,6}*144
12-fold quotients : {4,6,2}*96c
24-fold quotients : {4,3,2}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (  1, 39)(  2, 40)(  3, 37)(  4, 38)(  5, 43)(  6, 44)(  7, 41)(  8, 42)
(  9, 47)( 10, 48)( 11, 45)( 12, 46)( 13, 51)( 14, 52)( 15, 49)( 16, 50)
( 17, 55)( 18, 56)( 19, 53)( 20, 54)( 21, 59)( 22, 60)( 23, 57)( 24, 58)
( 25, 63)( 26, 64)( 27, 61)( 28, 62)( 29, 67)( 30, 68)( 31, 65)( 32, 66)
( 33, 71)( 34, 72)( 35, 69)( 36, 70)( 73,111)( 74,112)( 75,109)( 76,110)
( 77,115)( 78,116)( 79,113)( 80,114)( 81,119)( 82,120)( 83,117)( 84,118)
( 85,123)( 86,124)( 87,121)( 88,122)( 89,127)( 90,128)( 91,125)( 92,126)
( 93,131)( 94,132)( 95,129)( 96,130)( 97,135)( 98,136)( 99,133)(100,134)
(101,139)(102,140)(103,137)(104,138)(105,143)(106,144)(107,141)(108,142)
(145,183)(146,184)(147,181)(148,182)(149,187)(150,188)(151,185)(152,186)
(153,191)(154,192)(155,189)(156,190)(157,195)(158,196)(159,193)(160,194)
(161,199)(162,200)(163,197)(164,198)(165,203)(166,204)(167,201)(168,202)
(169,207)(170,208)(171,205)(172,206)(173,211)(174,212)(175,209)(176,210)
(177,215)(178,216)(179,213)(180,214)(217,255)(218,256)(219,253)(220,254)
(221,259)(222,260)(223,257)(224,258)(225,263)(226,264)(227,261)(228,262)
(229,267)(230,268)(231,265)(232,266)(233,271)(234,272)(235,269)(236,270)
(237,275)(238,276)(239,273)(240,274)(241,279)(242,280)(243,277)(244,278)
(245,283)(246,284)(247,281)(248,282)(249,287)(250,288)(251,285)(252,286);;
s1 := (  3,  4)(  5,  9)(  6, 10)(  7, 12)(  8, 11)( 13, 25)( 14, 26)( 15, 28)
( 16, 27)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 29)( 22, 30)( 23, 32)
( 24, 31)( 39, 40)( 41, 45)( 42, 46)( 43, 48)( 44, 47)( 49, 61)( 50, 62)
( 51, 64)( 52, 63)( 53, 69)( 54, 70)( 55, 72)( 56, 71)( 57, 65)( 58, 66)
( 59, 68)( 60, 67)( 73,109)( 74,110)( 75,112)( 76,111)( 77,117)( 78,118)
( 79,120)( 80,119)( 81,113)( 82,114)( 83,116)( 84,115)( 85,133)( 86,134)
( 87,136)( 88,135)( 89,141)( 90,142)( 91,144)( 92,143)( 93,137)( 94,138)
( 95,140)( 96,139)( 97,121)( 98,122)( 99,124)(100,123)(101,129)(102,130)
(103,132)(104,131)(105,125)(106,126)(107,128)(108,127)(145,217)(146,218)
(147,220)(148,219)(149,225)(150,226)(151,228)(152,227)(153,221)(154,222)
(155,224)(156,223)(157,241)(158,242)(159,244)(160,243)(161,249)(162,250)
(163,252)(164,251)(165,245)(166,246)(167,248)(168,247)(169,229)(170,230)
(171,232)(172,231)(173,237)(174,238)(175,240)(176,239)(177,233)(178,234)
(179,236)(180,235)(181,253)(182,254)(183,256)(184,255)(185,261)(186,262)
(187,264)(188,263)(189,257)(190,258)(191,260)(192,259)(193,277)(194,278)
(195,280)(196,279)(197,285)(198,286)(199,288)(200,287)(201,281)(202,282)
(203,284)(204,283)(205,265)(206,266)(207,268)(208,267)(209,273)(210,274)
(211,276)(212,275)(213,269)(214,270)(215,272)(216,271);;
s2 := (  1,161)(  2,164)(  3,163)(  4,162)(  5,157)(  6,160)(  7,159)(  8,158)
(  9,165)( 10,168)( 11,167)( 12,166)( 13,149)( 14,152)( 15,151)( 16,150)
( 17,145)( 18,148)( 19,147)( 20,146)( 21,153)( 22,156)( 23,155)( 24,154)
( 25,173)( 26,176)( 27,175)( 28,174)( 29,169)( 30,172)( 31,171)( 32,170)
( 33,177)( 34,180)( 35,179)( 36,178)( 37,197)( 38,200)( 39,199)( 40,198)
( 41,193)( 42,196)( 43,195)( 44,194)( 45,201)( 46,204)( 47,203)( 48,202)
( 49,185)( 50,188)( 51,187)( 52,186)( 53,181)( 54,184)( 55,183)( 56,182)
( 57,189)( 58,192)( 59,191)( 60,190)( 61,209)( 62,212)( 63,211)( 64,210)
( 65,205)( 66,208)( 67,207)( 68,206)( 69,213)( 70,216)( 71,215)( 72,214)
( 73,269)( 74,272)( 75,271)( 76,270)( 77,265)( 78,268)( 79,267)( 80,266)
( 81,273)( 82,276)( 83,275)( 84,274)( 85,257)( 86,260)( 87,259)( 88,258)
( 89,253)( 90,256)( 91,255)( 92,254)( 93,261)( 94,264)( 95,263)( 96,262)
( 97,281)( 98,284)( 99,283)(100,282)(101,277)(102,280)(103,279)(104,278)
(105,285)(106,288)(107,287)(108,286)(109,233)(110,236)(111,235)(112,234)
(113,229)(114,232)(115,231)(116,230)(117,237)(118,240)(119,239)(120,238)
(121,221)(122,224)(123,223)(124,222)(125,217)(126,220)(127,219)(128,218)
(129,225)(130,228)(131,227)(132,226)(133,245)(134,248)(135,247)(136,246)
(137,241)(138,244)(139,243)(140,242)(141,249)(142,252)(143,251)(144,250);;
s3 := (  5,  9)(  6, 10)(  7, 11)(  8, 12)( 17, 21)( 18, 22)( 19, 23)( 20, 24)
( 29, 33)( 30, 34)( 31, 35)( 32, 36)( 41, 45)( 42, 46)( 43, 47)( 44, 48)
( 53, 57)( 54, 58)( 55, 59)( 56, 60)( 65, 69)( 66, 70)( 67, 71)( 68, 72)
( 77, 81)( 78, 82)( 79, 83)( 80, 84)( 89, 93)( 90, 94)( 91, 95)( 92, 96)
(101,105)(102,106)(103,107)(104,108)(113,117)(114,118)(115,119)(116,120)
(125,129)(126,130)(127,131)(128,132)(137,141)(138,142)(139,143)(140,144)
(149,153)(150,154)(151,155)(152,156)(161,165)(162,166)(163,167)(164,168)
(173,177)(174,178)(175,179)(176,180)(185,189)(186,190)(187,191)(188,192)
(197,201)(198,202)(199,203)(200,204)(209,213)(210,214)(211,215)(212,216)
(221,225)(222,226)(223,227)(224,228)(233,237)(234,238)(235,239)(236,240)
(245,249)(246,250)(247,251)(248,252)(257,261)(258,262)(259,263)(260,264)
(269,273)(270,274)(271,275)(272,276)(281,285)(282,286)(283,287)(284,288);;
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,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s0 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(288)!(  1, 39)(  2, 40)(  3, 37)(  4, 38)(  5, 43)(  6, 44)(  7, 41)
(  8, 42)(  9, 47)( 10, 48)( 11, 45)( 12, 46)( 13, 51)( 14, 52)( 15, 49)
( 16, 50)( 17, 55)( 18, 56)( 19, 53)( 20, 54)( 21, 59)( 22, 60)( 23, 57)
( 24, 58)( 25, 63)( 26, 64)( 27, 61)( 28, 62)( 29, 67)( 30, 68)( 31, 65)
( 32, 66)( 33, 71)( 34, 72)( 35, 69)( 36, 70)( 73,111)( 74,112)( 75,109)
( 76,110)( 77,115)( 78,116)( 79,113)( 80,114)( 81,119)( 82,120)( 83,117)
( 84,118)( 85,123)( 86,124)( 87,121)( 88,122)( 89,127)( 90,128)( 91,125)
( 92,126)( 93,131)( 94,132)( 95,129)( 96,130)( 97,135)( 98,136)( 99,133)
(100,134)(101,139)(102,140)(103,137)(104,138)(105,143)(106,144)(107,141)
(108,142)(145,183)(146,184)(147,181)(148,182)(149,187)(150,188)(151,185)
(152,186)(153,191)(154,192)(155,189)(156,190)(157,195)(158,196)(159,193)
(160,194)(161,199)(162,200)(163,197)(164,198)(165,203)(166,204)(167,201)
(168,202)(169,207)(170,208)(171,205)(172,206)(173,211)(174,212)(175,209)
(176,210)(177,215)(178,216)(179,213)(180,214)(217,255)(218,256)(219,253)
(220,254)(221,259)(222,260)(223,257)(224,258)(225,263)(226,264)(227,261)
(228,262)(229,267)(230,268)(231,265)(232,266)(233,271)(234,272)(235,269)
(236,270)(237,275)(238,276)(239,273)(240,274)(241,279)(242,280)(243,277)
(244,278)(245,283)(246,284)(247,281)(248,282)(249,287)(250,288)(251,285)
(252,286);
s1 := Sym(288)!(  3,  4)(  5,  9)(  6, 10)(  7, 12)(  8, 11)( 13, 25)( 14, 26)
( 15, 28)( 16, 27)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 29)( 22, 30)
( 23, 32)( 24, 31)( 39, 40)( 41, 45)( 42, 46)( 43, 48)( 44, 47)( 49, 61)
( 50, 62)( 51, 64)( 52, 63)( 53, 69)( 54, 70)( 55, 72)( 56, 71)( 57, 65)
( 58, 66)( 59, 68)( 60, 67)( 73,109)( 74,110)( 75,112)( 76,111)( 77,117)
( 78,118)( 79,120)( 80,119)( 81,113)( 82,114)( 83,116)( 84,115)( 85,133)
( 86,134)( 87,136)( 88,135)( 89,141)( 90,142)( 91,144)( 92,143)( 93,137)
( 94,138)( 95,140)( 96,139)( 97,121)( 98,122)( 99,124)(100,123)(101,129)
(102,130)(103,132)(104,131)(105,125)(106,126)(107,128)(108,127)(145,217)
(146,218)(147,220)(148,219)(149,225)(150,226)(151,228)(152,227)(153,221)
(154,222)(155,224)(156,223)(157,241)(158,242)(159,244)(160,243)(161,249)
(162,250)(163,252)(164,251)(165,245)(166,246)(167,248)(168,247)(169,229)
(170,230)(171,232)(172,231)(173,237)(174,238)(175,240)(176,239)(177,233)
(178,234)(179,236)(180,235)(181,253)(182,254)(183,256)(184,255)(185,261)
(186,262)(187,264)(188,263)(189,257)(190,258)(191,260)(192,259)(193,277)
(194,278)(195,280)(196,279)(197,285)(198,286)(199,288)(200,287)(201,281)
(202,282)(203,284)(204,283)(205,265)(206,266)(207,268)(208,267)(209,273)
(210,274)(211,276)(212,275)(213,269)(214,270)(215,272)(216,271);
s2 := Sym(288)!(  1,161)(  2,164)(  3,163)(  4,162)(  5,157)(  6,160)(  7,159)
(  8,158)(  9,165)( 10,168)( 11,167)( 12,166)( 13,149)( 14,152)( 15,151)
( 16,150)( 17,145)( 18,148)( 19,147)( 20,146)( 21,153)( 22,156)( 23,155)
( 24,154)( 25,173)( 26,176)( 27,175)( 28,174)( 29,169)( 30,172)( 31,171)
( 32,170)( 33,177)( 34,180)( 35,179)( 36,178)( 37,197)( 38,200)( 39,199)
( 40,198)( 41,193)( 42,196)( 43,195)( 44,194)( 45,201)( 46,204)( 47,203)
( 48,202)( 49,185)( 50,188)( 51,187)( 52,186)( 53,181)( 54,184)( 55,183)
( 56,182)( 57,189)( 58,192)( 59,191)( 60,190)( 61,209)( 62,212)( 63,211)
( 64,210)( 65,205)( 66,208)( 67,207)( 68,206)( 69,213)( 70,216)( 71,215)
( 72,214)( 73,269)( 74,272)( 75,271)( 76,270)( 77,265)( 78,268)( 79,267)
( 80,266)( 81,273)( 82,276)( 83,275)( 84,274)( 85,257)( 86,260)( 87,259)
( 88,258)( 89,253)( 90,256)( 91,255)( 92,254)( 93,261)( 94,264)( 95,263)
( 96,262)( 97,281)( 98,284)( 99,283)(100,282)(101,277)(102,280)(103,279)
(104,278)(105,285)(106,288)(107,287)(108,286)(109,233)(110,236)(111,235)
(112,234)(113,229)(114,232)(115,231)(116,230)(117,237)(118,240)(119,239)
(120,238)(121,221)(122,224)(123,223)(124,222)(125,217)(126,220)(127,219)
(128,218)(129,225)(130,228)(131,227)(132,226)(133,245)(134,248)(135,247)
(136,246)(137,241)(138,244)(139,243)(140,242)(141,249)(142,252)(143,251)
(144,250);
s3 := Sym(288)!(  5,  9)(  6, 10)(  7, 11)(  8, 12)( 17, 21)( 18, 22)( 19, 23)
( 20, 24)( 29, 33)( 30, 34)( 31, 35)( 32, 36)( 41, 45)( 42, 46)( 43, 47)
( 44, 48)( 53, 57)( 54, 58)( 55, 59)( 56, 60)( 65, 69)( 66, 70)( 67, 71)
( 68, 72)( 77, 81)( 78, 82)( 79, 83)( 80, 84)( 89, 93)( 90, 94)( 91, 95)
( 92, 96)(101,105)(102,106)(103,107)(104,108)(113,117)(114,118)(115,119)
(116,120)(125,129)(126,130)(127,131)(128,132)(137,141)(138,142)(139,143)
(140,144)(149,153)(150,154)(151,155)(152,156)(161,165)(162,166)(163,167)
(164,168)(173,177)(174,178)(175,179)(176,180)(185,189)(186,190)(187,191)
(188,192)(197,201)(198,202)(199,203)(200,204)(209,213)(210,214)(211,215)
(212,216)(221,225)(222,226)(223,227)(224,228)(233,237)(234,238)(235,239)
(236,240)(245,249)(246,250)(247,251)(248,252)(257,261)(258,262)(259,263)
(260,264)(269,273)(270,274)(271,275)(272,276)(281,285)(282,286)(283,287)
(284,288);
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, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s0 >;

```
References : None.
to this polytope