Polytope of Type {48,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {48,10}*960
Also Known As : {48,10|2}. if this polytope has another name.
Group : SmallGroup(960,1009)
Rank : 3
Schlafli Type : {48,10}
Number of vertices, edges, etc : 48, 240, 10
Order of s₀s₁s₂ : 240
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {48,10,2} of size 1920
Vertex Figure Of :
   {2,48,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {24,10}*480
   3-fold quotients : {16,10}*320
   4-fold quotients : {12,10}*240
   5-fold quotients : {48,2}*192
   6-fold quotients : {8,10}*160
   8-fold quotients : {6,10}*120
   10-fold quotients : {24,2}*96
   12-fold quotients : {4,10}*80
   15-fold quotients : {16,2}*64
   20-fold quotients : {12,2}*48
   24-fold quotients : {2,10}*40
   30-fold quotients : {8,2}*32
   40-fold quotients : {6,2}*24
   48-fold quotients : {2,5}*20
   60-fold quotients : {4,2}*16
   80-fold quotients : {3,2}*12
   120-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {48,20}*1920a, {96,10}*1920
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)( 61, 91)( 62, 92)( 63, 93)( 64, 94)( 65, 95)( 66,101)( 67,102)
( 68,103)( 69,104)( 70,105)( 71, 96)( 72, 97)( 73, 98)( 74, 99)( 75,100)
( 76,106)( 77,107)( 78,108)( 79,109)( 80,110)( 81,116)( 82,117)( 83,118)
( 84,119)( 85,120)( 86,111)( 87,112)( 88,113)( 89,114)( 90,115)(121,181)
(122,182)(123,183)(124,184)(125,185)(126,191)(127,192)(128,193)(129,194)
(130,195)(131,186)(132,187)(133,188)(134,189)(135,190)(136,196)(137,197)
(138,198)(139,199)(140,200)(141,206)(142,207)(143,208)(144,209)(145,210)
(146,201)(147,202)(148,203)(149,204)(150,205)(151,226)(152,227)(153,228)
(154,229)(155,230)(156,236)(157,237)(158,238)(159,239)(160,240)(161,231)
(162,232)(163,233)(164,234)(165,235)(166,211)(167,212)(168,213)(169,214)
(170,215)(171,221)(172,222)(173,223)(174,224)(175,225)(176,216)(177,217)
(178,218)(179,219)(180,220);;
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)( 61,216)( 62,220)( 63,219)( 64,218)
( 65,217)( 66,211)( 67,215)( 68,214)( 69,213)( 70,212)( 71,221)( 72,225)
( 73,224)( 74,223)( 75,222)( 76,231)( 77,235)( 78,234)( 79,233)( 80,232)
( 81,226)( 82,230)( 83,229)( 84,228)( 85,227)( 86,236)( 87,240)( 88,239)
( 89,238)( 90,237)( 91,186)( 92,190)( 93,189)( 94,188)( 95,187)( 96,181)
( 97,185)( 98,184)( 99,183)(100,182)(101,191)(102,195)(103,194)(104,193)
(105,192)(106,201)(107,205)(108,204)(109,203)(110,202)(111,196)(112,200)
(113,199)(114,198)(115,197)(116,206)(117,210)(118,209)(119,208)(120,207);;
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)
(121,122)(123,125)(126,127)(128,130)(131,132)(133,135)(136,137)(138,140)
(141,142)(143,145)(146,147)(148,150)(151,152)(153,155)(156,157)(158,160)
(161,162)(163,165)(166,167)(168,170)(171,172)(173,175)(176,177)(178,180)
(181,182)(183,185)(186,187)(188,190)(191,192)(193,195)(196,197)(198,200)
(201,202)(203,205)(206,207)(208,210)(211,212)(213,215)(216,217)(218,220)
(221,222)(223,225)(226,227)(228,230)(231,232)(233,235)(236,237)(238,240);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, 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, 
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*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(240)!(  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)( 61, 91)( 62, 92)( 63, 93)( 64, 94)( 65, 95)( 66,101)
( 67,102)( 68,103)( 69,104)( 70,105)( 71, 96)( 72, 97)( 73, 98)( 74, 99)
( 75,100)( 76,106)( 77,107)( 78,108)( 79,109)( 80,110)( 81,116)( 82,117)
( 83,118)( 84,119)( 85,120)( 86,111)( 87,112)( 88,113)( 89,114)( 90,115)
(121,181)(122,182)(123,183)(124,184)(125,185)(126,191)(127,192)(128,193)
(129,194)(130,195)(131,186)(132,187)(133,188)(134,189)(135,190)(136,196)
(137,197)(138,198)(139,199)(140,200)(141,206)(142,207)(143,208)(144,209)
(145,210)(146,201)(147,202)(148,203)(149,204)(150,205)(151,226)(152,227)
(153,228)(154,229)(155,230)(156,236)(157,237)(158,238)(159,239)(160,240)
(161,231)(162,232)(163,233)(164,234)(165,235)(166,211)(167,212)(168,213)
(169,214)(170,215)(171,221)(172,222)(173,223)(174,224)(175,225)(176,216)
(177,217)(178,218)(179,219)(180,220);
s1 := Sym(240)!(  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)( 61,216)( 62,220)( 63,219)
( 64,218)( 65,217)( 66,211)( 67,215)( 68,214)( 69,213)( 70,212)( 71,221)
( 72,225)( 73,224)( 74,223)( 75,222)( 76,231)( 77,235)( 78,234)( 79,233)
( 80,232)( 81,226)( 82,230)( 83,229)( 84,228)( 85,227)( 86,236)( 87,240)
( 88,239)( 89,238)( 90,237)( 91,186)( 92,190)( 93,189)( 94,188)( 95,187)
( 96,181)( 97,185)( 98,184)( 99,183)(100,182)(101,191)(102,195)(103,194)
(104,193)(105,192)(106,201)(107,205)(108,204)(109,203)(110,202)(111,196)
(112,200)(113,199)(114,198)(115,197)(116,206)(117,210)(118,209)(119,208)
(120,207);
s2 := Sym(240)!(  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)(121,122)(123,125)(126,127)(128,130)(131,132)(133,135)(136,137)
(138,140)(141,142)(143,145)(146,147)(148,150)(151,152)(153,155)(156,157)
(158,160)(161,162)(163,165)(166,167)(168,170)(171,172)(173,175)(176,177)
(178,180)(181,182)(183,185)(186,187)(188,190)(191,192)(193,195)(196,197)
(198,200)(201,202)(203,205)(206,207)(208,210)(211,212)(213,215)(216,217)
(218,220)(221,222)(223,225)(226,227)(228,230)(231,232)(233,235)(236,237)
(238,240);
poly := sub<Sym(240)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, 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, 
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*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