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# Polytope of Type {12,12,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,12,4}*1152e
if this polytope has a name.
Group : SmallGroup(1152,156063)
Rank : 4
Schlafli Type : {12,12,4}
Number of vertices, edges, etc : 12, 72, 24, 4
Order of s0s1s2s3 : 12
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 : {6,12,4}*576e, {12,6,4}*576d
3-fold quotients : {4,12,4}*384c
4-fold quotients : {6,6,4}*288d
6-fold quotients : {2,12,4}*192c, {4,6,4}*192b
12-fold quotients : {2,6,4}*96c
24-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (  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)
(145,181)(146,182)(147,183)(148,184)(149,189)(150,190)(151,191)(152,192)
(153,185)(154,186)(155,187)(156,188)(157,193)(158,194)(159,195)(160,196)
(161,201)(162,202)(163,203)(164,204)(165,197)(166,198)(167,199)(168,200)
(169,205)(170,206)(171,207)(172,208)(173,213)(174,214)(175,215)(176,216)
(177,209)(178,210)(179,211)(180,212)(217,253)(218,254)(219,255)(220,256)
(221,261)(222,262)(223,263)(224,264)(225,257)(226,258)(227,259)(228,260)
(229,265)(230,266)(231,267)(232,268)(233,273)(234,274)(235,275)(236,276)
(237,269)(238,270)(239,271)(240,272)(241,277)(242,278)(243,279)(244,280)
(245,285)(246,286)(247,287)(248,288)(249,281)(250,282)(251,283)(252,284);;
s1 := (  1,149)(  2,150)(  3,152)(  4,151)(  5,145)(  6,146)(  7,148)(  8,147)
(  9,153)( 10,154)( 11,156)( 12,155)( 13,173)( 14,174)( 15,176)( 16,175)
( 17,169)( 18,170)( 19,172)( 20,171)( 21,177)( 22,178)( 23,180)( 24,179)
( 25,161)( 26,162)( 27,164)( 28,163)( 29,157)( 30,158)( 31,160)( 32,159)
( 33,165)( 34,166)( 35,168)( 36,167)( 37,185)( 38,186)( 39,188)( 40,187)
( 41,181)( 42,182)( 43,184)( 44,183)( 45,189)( 46,190)( 47,192)( 48,191)
( 49,209)( 50,210)( 51,212)( 52,211)( 53,205)( 54,206)( 55,208)( 56,207)
( 57,213)( 58,214)( 59,216)( 60,215)( 61,197)( 62,198)( 63,200)( 64,199)
( 65,193)( 66,194)( 67,196)( 68,195)( 69,201)( 70,202)( 71,204)( 72,203)
( 73,221)( 74,222)( 75,224)( 76,223)( 77,217)( 78,218)( 79,220)( 80,219)
( 81,225)( 82,226)( 83,228)( 84,227)( 85,245)( 86,246)( 87,248)( 88,247)
( 89,241)( 90,242)( 91,244)( 92,243)( 93,249)( 94,250)( 95,252)( 96,251)
( 97,233)( 98,234)( 99,236)(100,235)(101,229)(102,230)(103,232)(104,231)
(105,237)(106,238)(107,240)(108,239)(109,257)(110,258)(111,260)(112,259)
(113,253)(114,254)(115,256)(116,255)(117,261)(118,262)(119,264)(120,263)
(121,281)(122,282)(123,284)(124,283)(125,277)(126,278)(127,280)(128,279)
(129,285)(130,286)(131,288)(132,287)(133,269)(134,270)(135,272)(136,271)
(137,265)(138,266)(139,268)(140,267)(141,273)(142,274)(143,276)(144,275);;
s2 := (  1, 13)(  2, 16)(  3, 15)(  4, 14)(  5, 17)(  6, 20)(  7, 19)(  8, 18)
(  9, 21)( 10, 24)( 11, 23)( 12, 22)( 26, 28)( 30, 32)( 34, 36)( 37, 49)
( 38, 52)( 39, 51)( 40, 50)( 41, 53)( 42, 56)( 43, 55)( 44, 54)( 45, 57)
( 46, 60)( 47, 59)( 48, 58)( 62, 64)( 66, 68)( 70, 72)( 73, 85)( 74, 88)
( 75, 87)( 76, 86)( 77, 89)( 78, 92)( 79, 91)( 80, 90)( 81, 93)( 82, 96)
( 83, 95)( 84, 94)( 98,100)(102,104)(106,108)(109,121)(110,124)(111,123)
(112,122)(113,125)(114,128)(115,127)(116,126)(117,129)(118,132)(119,131)
(120,130)(134,136)(138,140)(142,144)(145,229)(146,232)(147,231)(148,230)
(149,233)(150,236)(151,235)(152,234)(153,237)(154,240)(155,239)(156,238)
(157,217)(158,220)(159,219)(160,218)(161,221)(162,224)(163,223)(164,222)
(165,225)(166,228)(167,227)(168,226)(169,241)(170,244)(171,243)(172,242)
(173,245)(174,248)(175,247)(176,246)(177,249)(178,252)(179,251)(180,250)
(181,265)(182,268)(183,267)(184,266)(185,269)(186,272)(187,271)(188,270)
(189,273)(190,276)(191,275)(192,274)(193,253)(194,256)(195,255)(196,254)
(197,257)(198,260)(199,259)(200,258)(201,261)(202,264)(203,263)(204,262)
(205,277)(206,280)(207,279)(208,278)(209,281)(210,284)(211,283)(212,282)
(213,285)(214,288)(215,287)(216,286);;
s3 := (  1, 74)(  2, 73)(  3, 76)(  4, 75)(  5, 78)(  6, 77)(  7, 80)(  8, 79)
(  9, 82)( 10, 81)( 11, 84)( 12, 83)( 13, 86)( 14, 85)( 15, 88)( 16, 87)
( 17, 90)( 18, 89)( 19, 92)( 20, 91)( 21, 94)( 22, 93)( 23, 96)( 24, 95)
( 25, 98)( 26, 97)( 27,100)( 28, 99)( 29,102)( 30,101)( 31,104)( 32,103)
( 33,106)( 34,105)( 35,108)( 36,107)( 37,110)( 38,109)( 39,112)( 40,111)
( 41,114)( 42,113)( 43,116)( 44,115)( 45,118)( 46,117)( 47,120)( 48,119)
( 49,122)( 50,121)( 51,124)( 52,123)( 53,126)( 54,125)( 55,128)( 56,127)
( 57,130)( 58,129)( 59,132)( 60,131)( 61,134)( 62,133)( 63,136)( 64,135)
( 65,138)( 66,137)( 67,140)( 68,139)( 69,142)( 70,141)( 71,144)( 72,143)
(145,218)(146,217)(147,220)(148,219)(149,222)(150,221)(151,224)(152,223)
(153,226)(154,225)(155,228)(156,227)(157,230)(158,229)(159,232)(160,231)
(161,234)(162,233)(163,236)(164,235)(165,238)(166,237)(167,240)(168,239)
(169,242)(170,241)(171,244)(172,243)(173,246)(174,245)(175,248)(176,247)
(177,250)(178,249)(179,252)(180,251)(181,254)(182,253)(183,256)(184,255)
(185,258)(186,257)(187,260)(188,259)(189,262)(190,261)(191,264)(192,263)
(193,266)(194,265)(195,268)(196,267)(197,270)(198,269)(199,272)(200,271)
(201,274)(202,273)(203,276)(204,275)(205,278)(206,277)(207,280)(208,279)
(209,282)(210,281)(211,284)(212,283)(213,286)(214,285)(215,288)(216,287);;
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*s2*s1*s0*s1*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s2*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope