Polytope of Type {2,24,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,24,20}*1920b
if this polytope has a name.
Group : SmallGroup(1920,150705)
Rank : 4
Schlafli Type : {2,24,20}
Number of vertices, edges, etc : 2, 24, 240, 20
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 : {2,12,20}*960
   3-fold quotients : {2,8,20}*640b
   4-fold quotients : {2,12,10}*480, {2,6,20}*480a
   5-fold quotients : {2,24,4}*384b
   6-fold quotients : {2,4,20}*320
   8-fold quotients : {2,6,10}*240
   10-fold quotients : {2,12,4}*192a
   12-fold quotients : {2,2,20}*160, {2,4,10}*160
   15-fold quotients : {2,8,4}*128b
   20-fold quotients : {2,12,2}*96, {2,6,4}*96a
   24-fold quotients : {2,2,10}*80
   30-fold quotients : {2,4,4}*64
   40-fold quotients : {2,6,2}*48
   48-fold quotients : {2,2,5}*40
   60-fold quotients : {2,2,4}*32, {2,4,2}*32
   80-fold quotients : {2,3,2}*24
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope