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Polytope of Type {2,48,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,48,10}*1920
if this polytope has a name.
Group : SmallGroup(1920,203905)
Rank : 4
Schlafli Type : {2,48,10}
Number of vertices, edges, etc : 2, 48, 240, 10
Order of s0s1s2s3 : 240
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 : {2,24,10}*960
   3-fold quotients : {2,16,10}*640
   4-fold quotients : {2,12,10}*480
   5-fold quotients : {2,48,2}*384
   6-fold quotients : {2,8,10}*320
   8-fold quotients : {2,6,10}*240
   10-fold quotients : {2,24,2}*192
   12-fold quotients : {2,4,10}*160
   15-fold quotients : {2,16,2}*128
   20-fold quotients : {2,12,2}*96
   24-fold quotients : {2,2,10}*80
   30-fold quotients : {2,8,2}*64
   40-fold quotients : {2,6,2}*48
   48-fold quotients : {2,2,5}*40
   60-fold quotients : {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, 93)( 64, 94)( 65, 95)( 66, 96)( 67, 97)( 68,103)( 69,104)
( 70,105)( 71,106)( 72,107)( 73, 98)( 74, 99)( 75,100)( 76,101)( 77,102)
( 78,108)( 79,109)( 80,110)( 81,111)( 82,112)( 83,118)( 84,119)( 85,120)
( 86,121)( 87,122)( 88,113)( 89,114)( 90,115)( 91,116)( 92,117)(123,183)
(124,184)(125,185)(126,186)(127,187)(128,193)(129,194)(130,195)(131,196)
(132,197)(133,188)(134,189)(135,190)(136,191)(137,192)(138,198)(139,199)
(140,200)(141,201)(142,202)(143,208)(144,209)(145,210)(146,211)(147,212)
(148,203)(149,204)(150,205)(151,206)(152,207)(153,228)(154,229)(155,230)
(156,231)(157,232)(158,238)(159,239)(160,240)(161,241)(162,242)(163,233)
(164,234)(165,235)(166,236)(167,237)(168,213)(169,214)(170,215)(171,216)
(172,217)(173,223)(174,224)(175,225)(176,226)(177,227)(178,218)(179,219)
(180,220)(181,221)(182,222);;
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)( 63,218)( 64,222)( 65,221)( 66,220)
( 67,219)( 68,213)( 69,217)( 70,216)( 71,215)( 72,214)( 73,223)( 74,227)
( 75,226)( 76,225)( 77,224)( 78,233)( 79,237)( 80,236)( 81,235)( 82,234)
( 83,228)( 84,232)( 85,231)( 86,230)( 87,229)( 88,238)( 89,242)( 90,241)
( 91,240)( 92,239)( 93,188)( 94,192)( 95,191)( 96,190)( 97,189)( 98,183)
( 99,187)(100,186)(101,185)(102,184)(103,193)(104,197)(105,196)(106,195)
(107,194)(108,203)(109,207)(110,206)(111,205)(112,204)(113,198)(114,202)
(115,201)(116,200)(117,199)(118,208)(119,212)(120,211)(121,210)(122,209);;
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, 34)( 35, 37)( 38, 39)( 40, 42)
( 43, 44)( 45, 47)( 48, 49)( 50, 52)( 53, 54)( 55, 57)( 58, 59)( 60, 62)
( 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, 94)( 95, 97)( 98, 99)(100,102)
(103,104)(105,107)(108,109)(110,112)(113,114)(115,117)(118,119)(120,122)
(123,124)(125,127)(128,129)(130,132)(133,134)(135,137)(138,139)(140,142)
(143,144)(145,147)(148,149)(150,152)(153,154)(155,157)(158,159)(160,162)
(163,164)(165,167)(168,169)(170,172)(173,174)(175,177)(178,179)(180,182)
(183,184)(185,187)(188,189)(190,192)(193,194)(195,197)(198,199)(200,202)
(203,204)(205,207)(208,209)(210,212)(213,214)(215,217)(218,219)(220,222)
(223,224)(225,227)(228,229)(230,232)(233,234)(235,237)(238,239)(240,242);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
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, 93)( 64, 94)( 65, 95)( 66, 96)( 67, 97)( 68,103)
( 69,104)( 70,105)( 71,106)( 72,107)( 73, 98)( 74, 99)( 75,100)( 76,101)
( 77,102)( 78,108)( 79,109)( 80,110)( 81,111)( 82,112)( 83,118)( 84,119)
( 85,120)( 86,121)( 87,122)( 88,113)( 89,114)( 90,115)( 91,116)( 92,117)
(123,183)(124,184)(125,185)(126,186)(127,187)(128,193)(129,194)(130,195)
(131,196)(132,197)(133,188)(134,189)(135,190)(136,191)(137,192)(138,198)
(139,199)(140,200)(141,201)(142,202)(143,208)(144,209)(145,210)(146,211)
(147,212)(148,203)(149,204)(150,205)(151,206)(152,207)(153,228)(154,229)
(155,230)(156,231)(157,232)(158,238)(159,239)(160,240)(161,241)(162,242)
(163,233)(164,234)(165,235)(166,236)(167,237)(168,213)(169,214)(170,215)
(171,216)(172,217)(173,223)(174,224)(175,225)(176,226)(177,227)(178,218)
(179,219)(180,220)(181,221)(182,222);
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)( 63,218)( 64,222)( 65,221)
( 66,220)( 67,219)( 68,213)( 69,217)( 70,216)( 71,215)( 72,214)( 73,223)
( 74,227)( 75,226)( 76,225)( 77,224)( 78,233)( 79,237)( 80,236)( 81,235)
( 82,234)( 83,228)( 84,232)( 85,231)( 86,230)( 87,229)( 88,238)( 89,242)
( 90,241)( 91,240)( 92,239)( 93,188)( 94,192)( 95,191)( 96,190)( 97,189)
( 98,183)( 99,187)(100,186)(101,185)(102,184)(103,193)(104,197)(105,196)
(106,195)(107,194)(108,203)(109,207)(110,206)(111,205)(112,204)(113,198)
(114,202)(115,201)(116,200)(117,199)(118,208)(119,212)(120,211)(121,210)
(122,209);
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, 34)( 35, 37)( 38, 39)
( 40, 42)( 43, 44)( 45, 47)( 48, 49)( 50, 52)( 53, 54)( 55, 57)( 58, 59)
( 60, 62)( 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, 94)( 95, 97)( 98, 99)
(100,102)(103,104)(105,107)(108,109)(110,112)(113,114)(115,117)(118,119)
(120,122)(123,124)(125,127)(128,129)(130,132)(133,134)(135,137)(138,139)
(140,142)(143,144)(145,147)(148,149)(150,152)(153,154)(155,157)(158,159)
(160,162)(163,164)(165,167)(168,169)(170,172)(173,174)(175,177)(178,179)
(180,182)(183,184)(185,187)(188,189)(190,192)(193,194)(195,197)(198,199)
(200,202)(203,204)(205,207)(208,209)(210,212)(213,214)(215,217)(218,219)
(220,222)(223,224)(225,227)(228,229)(230,232)(233,234)(235,237)(238,239)
(240,242);
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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

to this polytope