Polytope of Type {28,4,3} with group SmallGroup(1344,11328)

Overview

Group: SmallGroup(1344,11328)
Rank: 4
Schläfli Type: {28,4,3}
Vertices, edges, …: 28, 112, 12, 6
Order of s₀s₁s₂s₃: 84
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: {{28,4|2},{4,3}}. if this polytope has another name.

Special Properties

Universal
Orientable
Flat

Quotients maximal quotients in bold

2-fold

{14,4,3}*672

4-fold

{28,2,3}*336

7-fold

{4,4,3}*192b

8-fold

{14,2,3}*168

14-fold

{2,4,3}*96

16-fold

{7,2,3}*84

28-fold

56-fold

{2,2,3}*24

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)^2> of order 2

4 facets

2 of {28,2}*112
2 of {28,4}*224

28 vertex figures

28 of 2-fold non-regular quotient of {4,3}*48

Representations

Permutation Representation (GAP)

s0 := (  5, 25)(  6, 26)(  7, 27)(  8, 28)(  9, 21)( 10, 22)( 11, 23)( 12, 24)( 13, 17)( 14, 18)( 15, 19)( 16, 20)( 33, 53)( 34, 54)( 35, 55)( 36, 56)( 37, 49)( 38, 50)( 39, 51)( 40, 52)( 41, 45)( 42, 46)( 43, 47)( 44, 48)( 61, 81)( 62, 82)( 63, 83)( 64, 84)( 65, 77)( 66, 78)( 67, 79)( 68, 80)( 69, 73)( 70, 74)( 71, 75)( 72, 76)( 89,109)( 90,110)( 91,111)( 92,112)( 93,105)( 94,106)( 95,107)( 96,108)( 97,101)( 98,102)( 99,103)(100,104)(117,137)(118,138)(119,139)(120,140)(121,133)(122,134)(123,135)(124,136)(125,129)(126,130)(127,131)(128,132)(145,165)(146,166)(147,167)(148,168)(149,161)(150,162)(151,163)(152,164)(153,157)(154,158)(155,159)(156,160)(169,253)(170,254)(171,255)(172,256)(173,277)(174,278)(175,279)(176,280)(177,273)(178,274)(179,275)(180,276)(181,269)(182,270)(183,271)(184,272)(185,265)(186,266)(187,267)(188,268)(189,261)(190,262)(191,263)(192,264)(193,257)(194,258)(195,259)(196,260)(197,281)(198,282)(199,283)(200,284)(201,305)(202,306)(203,307)(204,308)(205,301)(206,302)(207,303)(208,304)(209,297)(210,298)(211,299)(212,300)(213,293)(214,294)(215,295)(216,296)(217,289)(218,290)(219,291)(220,292)(221,285)(222,286)(223,287)(224,288)(225,309)(226,310)(227,311)(228,312)(229,333)(230,334)(231,335)(232,336)(233,329)(234,330)(235,331)(236,332)(237,325)(238,326)(239,327)(240,328)(241,321)(242,322)(243,323)(244,324)(245,317)(246,318)(247,319)(248,320)(249,313)(250,314)(251,315)(252,316);;
s1 := (  1,175)(  2,176)(  3,173)(  4,174)(  5,171)(  6,172)(  7,169)(  8,170)(  9,195)( 10,196)( 11,193)( 12,194)( 13,191)( 14,192)( 15,189)( 16,190)( 17,187)( 18,188)( 19,185)( 20,186)( 21,183)( 22,184)( 23,181)( 24,182)( 25,179)( 26,180)( 27,177)( 28,178)( 29,203)( 30,204)( 31,201)( 32,202)( 33,199)( 34,200)( 35,197)( 36,198)( 37,223)( 38,224)( 39,221)( 40,222)( 41,219)( 42,220)( 43,217)( 44,218)( 45,215)( 46,216)( 47,213)( 48,214)( 49,211)( 50,212)( 51,209)( 52,210)( 53,207)( 54,208)( 55,205)( 56,206)( 57,231)( 58,232)( 59,229)( 60,230)( 61,227)( 62,228)( 63,225)( 64,226)( 65,251)( 66,252)( 67,249)( 68,250)( 69,247)( 70,248)( 71,245)( 72,246)( 73,243)( 74,244)( 75,241)( 76,242)( 77,239)( 78,240)( 79,237)( 80,238)( 81,235)( 82,236)( 83,233)( 84,234)( 85,259)( 86,260)( 87,257)( 88,258)( 89,255)( 90,256)( 91,253)( 92,254)( 93,279)( 94,280)( 95,277)( 96,278)( 97,275)( 98,276)( 99,273)(100,274)(101,271)(102,272)(103,269)(104,270)(105,267)(106,268)(107,265)(108,266)(109,263)(110,264)(111,261)(112,262)(113,287)(114,288)(115,285)(116,286)(117,283)(118,284)(119,281)(120,282)(121,307)(122,308)(123,305)(124,306)(125,303)(126,304)(127,301)(128,302)(129,299)(130,300)(131,297)(132,298)(133,295)(134,296)(135,293)(136,294)(137,291)(138,292)(139,289)(140,290)(141,315)(142,316)(143,313)(144,314)(145,311)(146,312)(147,309)(148,310)(149,335)(150,336)(151,333)(152,334)(153,331)(154,332)(155,329)(156,330)(157,327)(158,328)(159,325)(160,326)(161,323)(162,324)(163,321)(164,322)(165,319)(166,320)(167,317)(168,318);;
s2 := (  3,  4)(  7,  8)( 11, 12)( 15, 16)( 19, 20)( 23, 24)( 27, 28)( 29, 57)( 30, 58)( 31, 60)( 32, 59)( 33, 61)( 34, 62)( 35, 64)( 36, 63)( 37, 65)( 38, 66)( 39, 68)( 40, 67)( 41, 69)( 42, 70)( 43, 72)( 44, 71)( 45, 73)( 46, 74)( 47, 76)( 48, 75)( 49, 77)( 50, 78)( 51, 80)( 52, 79)( 53, 81)( 54, 82)( 55, 84)( 56, 83)( 87, 88)( 91, 92)( 95, 96)( 99,100)(103,104)(107,108)(111,112)(113,141)(114,142)(115,144)(116,143)(117,145)(118,146)(119,148)(120,147)(121,149)(122,150)(123,152)(124,151)(125,153)(126,154)(127,156)(128,155)(129,157)(130,158)(131,160)(132,159)(133,161)(134,162)(135,164)(136,163)(137,165)(138,166)(139,168)(140,167)(171,172)(175,176)(179,180)(183,184)(187,188)(191,192)(195,196)(197,225)(198,226)(199,228)(200,227)(201,229)(202,230)(203,232)(204,231)(205,233)(206,234)(207,236)(208,235)(209,237)(210,238)(211,240)(212,239)(213,241)(214,242)(215,244)(216,243)(217,245)(218,246)(219,248)(220,247)(221,249)(222,250)(223,252)(224,251)(255,256)(259,260)(263,264)(267,268)(271,272)(275,276)(279,280)(281,309)(282,310)(283,312)(284,311)(285,313)(286,314)(287,316)(288,315)(289,317)(290,318)(291,320)(292,319)(293,321)(294,322)(295,324)(296,323)(297,325)(298,326)(299,328)(300,327)(301,329)(302,330)(303,332)(304,331)(305,333)(306,334)(307,336)(308,335);;
s3 := (  1, 29)(  2, 32)(  3, 31)(  4, 30)(  5, 33)(  6, 36)(  7, 35)(  8, 34)(  9, 37)( 10, 40)( 11, 39)( 12, 38)( 13, 41)( 14, 44)( 15, 43)( 16, 42)( 17, 45)( 18, 48)( 19, 47)( 20, 46)( 21, 49)( 22, 52)( 23, 51)( 24, 50)( 25, 53)( 26, 56)( 27, 55)( 28, 54)( 58, 60)( 62, 64)( 66, 68)( 70, 72)( 74, 76)( 78, 80)( 82, 84)( 85,113)( 86,116)( 87,115)( 88,114)( 89,117)( 90,120)( 91,119)( 92,118)( 93,121)( 94,124)( 95,123)( 96,122)( 97,125)( 98,128)( 99,127)(100,126)(101,129)(102,132)(103,131)(104,130)(105,133)(106,136)(107,135)(108,134)(109,137)(110,140)(111,139)(112,138)(142,144)(146,148)(150,152)(154,156)(158,160)(162,164)(166,168)(169,197)(170,200)(171,199)(172,198)(173,201)(174,204)(175,203)(176,202)(177,205)(178,208)(179,207)(180,206)(181,209)(182,212)(183,211)(184,210)(185,213)(186,216)(187,215)(188,214)(189,217)(190,220)(191,219)(192,218)(193,221)(194,224)(195,223)(196,222)(226,228)(230,232)(234,236)(238,240)(242,244)(246,248)(250,252)(253,281)(254,284)(255,283)(256,282)(257,285)(258,288)(259,287)(260,286)(261,289)(262,292)(263,291)(264,290)(265,293)(266,296)(267,295)(268,294)(269,297)(270,300)(271,299)(272,298)(273,301)(274,304)(275,303)(276,302)(277,305)(278,308)(279,307)(280,306)(310,312)(314,316)(318,320)(322,324)(326,328)(330,332)(334,336);;
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*s2*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*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*s0*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*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(336)!(  5, 25)(  6, 26)(  7, 27)(  8, 28)(  9, 21)( 10, 22)( 11, 23)( 12, 24)( 13, 17)( 14, 18)( 15, 19)( 16, 20)( 33, 53)( 34, 54)( 35, 55)( 36, 56)( 37, 49)( 38, 50)( 39, 51)( 40, 52)( 41, 45)( 42, 46)( 43, 47)( 44, 48)( 61, 81)( 62, 82)( 63, 83)( 64, 84)( 65, 77)( 66, 78)( 67, 79)( 68, 80)( 69, 73)( 70, 74)( 71, 75)( 72, 76)( 89,109)( 90,110)( 91,111)( 92,112)( 93,105)( 94,106)( 95,107)( 96,108)( 97,101)( 98,102)( 99,103)(100,104)(117,137)(118,138)(119,139)(120,140)(121,133)(122,134)(123,135)(124,136)(125,129)(126,130)(127,131)(128,132)(145,165)(146,166)(147,167)(148,168)(149,161)(150,162)(151,163)(152,164)(153,157)(154,158)(155,159)(156,160)(169,253)(170,254)(171,255)(172,256)(173,277)(174,278)(175,279)(176,280)(177,273)(178,274)(179,275)(180,276)(181,269)(182,270)(183,271)(184,272)(185,265)(186,266)(187,267)(188,268)(189,261)(190,262)(191,263)(192,264)(193,257)(194,258)(195,259)(196,260)(197,281)(198,282)(199,283)(200,284)(201,305)(202,306)(203,307)(204,308)(205,301)(206,302)(207,303)(208,304)(209,297)(210,298)(211,299)(212,300)(213,293)(214,294)(215,295)(216,296)(217,289)(218,290)(219,291)(220,292)(221,285)(222,286)(223,287)(224,288)(225,309)(226,310)(227,311)(228,312)(229,333)(230,334)(231,335)(232,336)(233,329)(234,330)(235,331)(236,332)(237,325)(238,326)(239,327)(240,328)(241,321)(242,322)(243,323)(244,324)(245,317)(246,318)(247,319)(248,320)(249,313)(250,314)(251,315)(252,316);
s1 := Sym(336)!(  1,175)(  2,176)(  3,173)(  4,174)(  5,171)(  6,172)(  7,169)(  8,170)(  9,195)( 10,196)( 11,193)( 12,194)( 13,191)( 14,192)( 15,189)( 16,190)( 17,187)( 18,188)( 19,185)( 20,186)( 21,183)( 22,184)( 23,181)( 24,182)( 25,179)( 26,180)( 27,177)( 28,178)( 29,203)( 30,204)( 31,201)( 32,202)( 33,199)( 34,200)( 35,197)( 36,198)( 37,223)( 38,224)( 39,221)( 40,222)( 41,219)( 42,220)( 43,217)( 44,218)( 45,215)( 46,216)( 47,213)( 48,214)( 49,211)( 50,212)( 51,209)( 52,210)( 53,207)( 54,208)( 55,205)( 56,206)( 57,231)( 58,232)( 59,229)( 60,230)( 61,227)( 62,228)( 63,225)( 64,226)( 65,251)( 66,252)( 67,249)( 68,250)( 69,247)( 70,248)( 71,245)( 72,246)( 73,243)( 74,244)( 75,241)( 76,242)( 77,239)( 78,240)( 79,237)( 80,238)( 81,235)( 82,236)( 83,233)( 84,234)( 85,259)( 86,260)( 87,257)( 88,258)( 89,255)( 90,256)( 91,253)( 92,254)( 93,279)( 94,280)( 95,277)( 96,278)( 97,275)( 98,276)( 99,273)(100,274)(101,271)(102,272)(103,269)(104,270)(105,267)(106,268)(107,265)(108,266)(109,263)(110,264)(111,261)(112,262)(113,287)(114,288)(115,285)(116,286)(117,283)(118,284)(119,281)(120,282)(121,307)(122,308)(123,305)(124,306)(125,303)(126,304)(127,301)(128,302)(129,299)(130,300)(131,297)(132,298)(133,295)(134,296)(135,293)(136,294)(137,291)(138,292)(139,289)(140,290)(141,315)(142,316)(143,313)(144,314)(145,311)(146,312)(147,309)(148,310)(149,335)(150,336)(151,333)(152,334)(153,331)(154,332)(155,329)(156,330)(157,327)(158,328)(159,325)(160,326)(161,323)(162,324)(163,321)(164,322)(165,319)(166,320)(167,317)(168,318);
s2 := Sym(336)!(  3,  4)(  7,  8)( 11, 12)( 15, 16)( 19, 20)( 23, 24)( 27, 28)( 29, 57)( 30, 58)( 31, 60)( 32, 59)( 33, 61)( 34, 62)( 35, 64)( 36, 63)( 37, 65)( 38, 66)( 39, 68)( 40, 67)( 41, 69)( 42, 70)( 43, 72)( 44, 71)( 45, 73)( 46, 74)( 47, 76)( 48, 75)( 49, 77)( 50, 78)( 51, 80)( 52, 79)( 53, 81)( 54, 82)( 55, 84)( 56, 83)( 87, 88)( 91, 92)( 95, 96)( 99,100)(103,104)(107,108)(111,112)(113,141)(114,142)(115,144)(116,143)(117,145)(118,146)(119,148)(120,147)(121,149)(122,150)(123,152)(124,151)(125,153)(126,154)(127,156)(128,155)(129,157)(130,158)(131,160)(132,159)(133,161)(134,162)(135,164)(136,163)(137,165)(138,166)(139,168)(140,167)(171,172)(175,176)(179,180)(183,184)(187,188)(191,192)(195,196)(197,225)(198,226)(199,228)(200,227)(201,229)(202,230)(203,232)(204,231)(205,233)(206,234)(207,236)(208,235)(209,237)(210,238)(211,240)(212,239)(213,241)(214,242)(215,244)(216,243)(217,245)(218,246)(219,248)(220,247)(221,249)(222,250)(223,252)(224,251)(255,256)(259,260)(263,264)(267,268)(271,272)(275,276)(279,280)(281,309)(282,310)(283,312)(284,311)(285,313)(286,314)(287,316)(288,315)(289,317)(290,318)(291,320)(292,319)(293,321)(294,322)(295,324)(296,323)(297,325)(298,326)(299,328)(300,327)(301,329)(302,330)(303,332)(304,331)(305,333)(306,334)(307,336)(308,335);
s3 := Sym(336)!(  1, 29)(  2, 32)(  3, 31)(  4, 30)(  5, 33)(  6, 36)(  7, 35)(  8, 34)(  9, 37)( 10, 40)( 11, 39)( 12, 38)( 13, 41)( 14, 44)( 15, 43)( 16, 42)( 17, 45)( 18, 48)( 19, 47)( 20, 46)( 21, 49)( 22, 52)( 23, 51)( 24, 50)( 25, 53)( 26, 56)( 27, 55)( 28, 54)( 58, 60)( 62, 64)( 66, 68)( 70, 72)( 74, 76)( 78, 80)( 82, 84)( 85,113)( 86,116)( 87,115)( 88,114)( 89,117)( 90,120)( 91,119)( 92,118)( 93,121)( 94,124)( 95,123)( 96,122)( 97,125)( 98,128)( 99,127)(100,126)(101,129)(102,132)(103,131)(104,130)(105,133)(106,136)(107,135)(108,134)(109,137)(110,140)(111,139)(112,138)(142,144)(146,148)(150,152)(154,156)(158,160)(162,164)(166,168)(169,197)(170,200)(171,199)(172,198)(173,201)(174,204)(175,203)(176,202)(177,205)(178,208)(179,207)(180,206)(181,209)(182,212)(183,211)(184,210)(185,213)(186,216)(187,215)(188,214)(189,217)(190,220)(191,219)(192,218)(193,221)(194,224)(195,223)(196,222)(226,228)(230,232)(234,236)(238,240)(242,244)(246,248)(250,252)(253,281)(254,284)(255,283)(256,282)(257,285)(258,288)(259,287)(260,286)(261,289)(262,292)(263,291)(264,290)(265,293)(266,296)(267,295)(268,294)(269,297)(270,300)(271,299)(272,298)(273,301)(274,304)(275,303)(276,302)(277,305)(278,308)(279,307)(280,306)(310,312)(314,316)(318,320)(322,324)(326,328)(330,332)(334,336);
poly := sub<Sym(336)|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*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*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*s0*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*s0*s1*s0*s1 >;

References

None.

to this polytope.