Polytope of Type {2,10,48}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,48}*1920
if this polytope has a name.
Group : SmallGroup(1920,203905)
Rank : 4
Schlafli Type : {2,10,48}
Number of vertices, edges, etc : 2, 10, 240, 48
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 : {2,10,24}*960
   3-fold quotients : {2,10,16}*640
   4-fold quotients : {2,10,12}*480
   5-fold quotients : {2,2,48}*384
   6-fold quotients : {2,10,8}*320
   8-fold quotients : {2,10,6}*240
   10-fold quotients : {2,2,24}*192
   12-fold quotients : {2,10,4}*160
   15-fold quotients : {2,2,16}*128
   20-fold quotients : {2,2,12}*96
   24-fold quotients : {2,10,2}*80
   30-fold quotients : {2,2,8}*64
   40-fold quotients : {2,2,6}*48
   48-fold quotients : {2,5,2}*40
   60-fold quotients : {2,2,4}*32
   80-fold quotients : {2,2,3}*24
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

to this polytope