Polytope of Type {24,20,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,20,2}*1920a
if this polytope has a name.
Group : SmallGroup(1920,148923)
Rank : 4
Schlafli Type : {24,20,2}
Number of vertices, edges, etc : 24, 240, 20, 2
Order of s₀s₁s₂s₃ : 120
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   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 : {24,10,2}*960, {12,20,2}*960
   3-fold quotients : {8,20,2}*640a
   4-fold quotients : {12,10,2}*480, {6,20,2}*480a
   5-fold quotients : {24,4,2}*384a
   6-fold quotients : {4,20,2}*320, {8,10,2}*320
   8-fold quotients : {6,10,2}*240
   10-fold quotients : {12,4,2}*192a, {24,2,2}*192
   12-fold quotients : {2,20,2}*160, {4,10,2}*160
   15-fold quotients : {8,4,2}*128a
   20-fold quotients : {12,2,2}*96, {6,4,2}*96a
   24-fold quotients : {2,10,2}*80
   30-fold quotients : {4,4,2}*64, {8,2,2}*64
   40-fold quotients : {6,2,2}*48
   48-fold quotients : {2,5,2}*40
   60-fold quotients : {2,4,2}*32, {4,2,2}*32
   80-fold quotients : {3,2,2}*24
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope