Polytope of Type {10,48}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,48}*960
Also Known As : {10,48|2}. if this polytope has another name.
Group : SmallGroup(960,1009)
Rank : 3
Schlafli Type : {10,48}
Number of vertices, edges, etc : 10, 240, 48
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 :
{10,48,2} of size 1920
Vertex Figure Of :
{2,10,48} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {10,24}*480
3-fold quotients : {10,16}*320
4-fold quotients : {10,12}*240
5-fold quotients : {2,48}*192
6-fold quotients : {10,8}*160
8-fold quotients : {10,6}*120
10-fold quotients : {2,24}*96
12-fold quotients : {10,4}*80
15-fold quotients : {2,16}*64
20-fold quotients : {2,12}*48
24-fold quotients : {10,2}*40
30-fold quotients : {2,8}*32
40-fold quotients : {2,6}*24
48-fold quotients : {5,2}*20
60-fold quotients : {2,4}*16
80-fold quotients : {2,3}*12
120-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {20,48}*1920a, {10,96}*1920
Permutation Representation (GAP) :
s0 := ( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)
( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)( 38, 39)
( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)( 58, 59)
( 62, 65)( 63, 64)( 67, 70)( 68, 69)( 72, 75)( 73, 74)( 77, 80)( 78, 79)
( 82, 85)( 83, 84)( 87, 90)( 88, 89)( 92, 95)( 93, 94)( 97,100)( 98, 99)
(102,105)(103,104)(107,110)(108,109)(112,115)(113,114)(117,120)(118,119)
(122,125)(123,124)(127,130)(128,129)(132,135)(133,134)(137,140)(138,139)
(142,145)(143,144)(147,150)(148,149)(152,155)(153,154)(157,160)(158,159)
(162,165)(163,164)(167,170)(168,169)(172,175)(173,174)(177,180)(178,179)
(182,185)(183,184)(187,190)(188,189)(192,195)(193,194)(197,200)(198,199)
(202,205)(203,204)(207,210)(208,209)(212,215)(213,214)(217,220)(218,219)
(222,225)(223,224)(227,230)(228,229)(232,235)(233,234)(237,240)(238,239);;
s1 := ( 1, 2)( 3, 5)( 6, 12)( 7, 11)( 8, 15)( 9, 14)( 10, 13)( 16, 17)
( 18, 20)( 21, 27)( 22, 26)( 23, 30)( 24, 29)( 25, 28)( 31, 47)( 32, 46)
( 33, 50)( 34, 49)( 35, 48)( 36, 57)( 37, 56)( 38, 60)( 39, 59)( 40, 58)
( 41, 52)( 42, 51)( 43, 55)( 44, 54)( 45, 53)( 61, 92)( 62, 91)( 63, 95)
( 64, 94)( 65, 93)( 66,102)( 67,101)( 68,105)( 69,104)( 70,103)( 71, 97)
( 72, 96)( 73,100)( 74, 99)( 75, 98)( 76,107)( 77,106)( 78,110)( 79,109)
( 80,108)( 81,117)( 82,116)( 83,120)( 84,119)( 85,118)( 86,112)( 87,111)
( 88,115)( 89,114)( 90,113)(121,182)(122,181)(123,185)(124,184)(125,183)
(126,192)(127,191)(128,195)(129,194)(130,193)(131,187)(132,186)(133,190)
(134,189)(135,188)(136,197)(137,196)(138,200)(139,199)(140,198)(141,207)
(142,206)(143,210)(144,209)(145,208)(146,202)(147,201)(148,205)(149,204)
(150,203)(151,227)(152,226)(153,230)(154,229)(155,228)(156,237)(157,236)
(158,240)(159,239)(160,238)(161,232)(162,231)(163,235)(164,234)(165,233)
(166,212)(167,211)(168,215)(169,214)(170,213)(171,222)(172,221)(173,225)
(174,224)(175,223)(176,217)(177,216)(178,220)(179,219)(180,218);;
s2 := ( 1,126)( 2,127)( 3,128)( 4,129)( 5,130)( 6,121)( 7,122)( 8,123)
( 9,124)( 10,125)( 11,131)( 12,132)( 13,133)( 14,134)( 15,135)( 16,141)
( 17,142)( 18,143)( 19,144)( 20,145)( 21,136)( 22,137)( 23,138)( 24,139)
( 25,140)( 26,146)( 27,147)( 28,148)( 29,149)( 30,150)( 31,171)( 32,172)
( 33,173)( 34,174)( 35,175)( 36,166)( 37,167)( 38,168)( 39,169)( 40,170)
( 41,176)( 42,177)( 43,178)( 44,179)( 45,180)( 46,156)( 47,157)( 48,158)
( 49,159)( 50,160)( 51,151)( 52,152)( 53,153)( 54,154)( 55,155)( 56,161)
( 57,162)( 58,163)( 59,164)( 60,165)( 61,216)( 62,217)( 63,218)( 64,219)
( 65,220)( 66,211)( 67,212)( 68,213)( 69,214)( 70,215)( 71,221)( 72,222)
( 73,223)( 74,224)( 75,225)( 76,231)( 77,232)( 78,233)( 79,234)( 80,235)
( 81,226)( 82,227)( 83,228)( 84,229)( 85,230)( 86,236)( 87,237)( 88,238)
( 89,239)( 90,240)( 91,186)( 92,187)( 93,188)( 94,189)( 95,190)( 96,181)
( 97,182)( 98,183)( 99,184)(100,185)(101,191)(102,192)(103,193)(104,194)
(105,195)(106,201)(107,202)(108,203)(109,204)(110,205)(111,196)(112,197)
(113,198)(114,199)(115,200)(116,206)(117,207)(118,208)(119,209)(120,210);;
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*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(240)!( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)
( 18, 19)( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)
( 38, 39)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)
( 58, 59)( 62, 65)( 63, 64)( 67, 70)( 68, 69)( 72, 75)( 73, 74)( 77, 80)
( 78, 79)( 82, 85)( 83, 84)( 87, 90)( 88, 89)( 92, 95)( 93, 94)( 97,100)
( 98, 99)(102,105)(103,104)(107,110)(108,109)(112,115)(113,114)(117,120)
(118,119)(122,125)(123,124)(127,130)(128,129)(132,135)(133,134)(137,140)
(138,139)(142,145)(143,144)(147,150)(148,149)(152,155)(153,154)(157,160)
(158,159)(162,165)(163,164)(167,170)(168,169)(172,175)(173,174)(177,180)
(178,179)(182,185)(183,184)(187,190)(188,189)(192,195)(193,194)(197,200)
(198,199)(202,205)(203,204)(207,210)(208,209)(212,215)(213,214)(217,220)
(218,219)(222,225)(223,224)(227,230)(228,229)(232,235)(233,234)(237,240)
(238,239);
s1 := Sym(240)!( 1, 2)( 3, 5)( 6, 12)( 7, 11)( 8, 15)( 9, 14)( 10, 13)
( 16, 17)( 18, 20)( 21, 27)( 22, 26)( 23, 30)( 24, 29)( 25, 28)( 31, 47)
( 32, 46)( 33, 50)( 34, 49)( 35, 48)( 36, 57)( 37, 56)( 38, 60)( 39, 59)
( 40, 58)( 41, 52)( 42, 51)( 43, 55)( 44, 54)( 45, 53)( 61, 92)( 62, 91)
( 63, 95)( 64, 94)( 65, 93)( 66,102)( 67,101)( 68,105)( 69,104)( 70,103)
( 71, 97)( 72, 96)( 73,100)( 74, 99)( 75, 98)( 76,107)( 77,106)( 78,110)
( 79,109)( 80,108)( 81,117)( 82,116)( 83,120)( 84,119)( 85,118)( 86,112)
( 87,111)( 88,115)( 89,114)( 90,113)(121,182)(122,181)(123,185)(124,184)
(125,183)(126,192)(127,191)(128,195)(129,194)(130,193)(131,187)(132,186)
(133,190)(134,189)(135,188)(136,197)(137,196)(138,200)(139,199)(140,198)
(141,207)(142,206)(143,210)(144,209)(145,208)(146,202)(147,201)(148,205)
(149,204)(150,203)(151,227)(152,226)(153,230)(154,229)(155,228)(156,237)
(157,236)(158,240)(159,239)(160,238)(161,232)(162,231)(163,235)(164,234)
(165,233)(166,212)(167,211)(168,215)(169,214)(170,213)(171,222)(172,221)
(173,225)(174,224)(175,223)(176,217)(177,216)(178,220)(179,219)(180,218);
s2 := Sym(240)!( 1,126)( 2,127)( 3,128)( 4,129)( 5,130)( 6,121)( 7,122)
( 8,123)( 9,124)( 10,125)( 11,131)( 12,132)( 13,133)( 14,134)( 15,135)
( 16,141)( 17,142)( 18,143)( 19,144)( 20,145)( 21,136)( 22,137)( 23,138)
( 24,139)( 25,140)( 26,146)( 27,147)( 28,148)( 29,149)( 30,150)( 31,171)
( 32,172)( 33,173)( 34,174)( 35,175)( 36,166)( 37,167)( 38,168)( 39,169)
( 40,170)( 41,176)( 42,177)( 43,178)( 44,179)( 45,180)( 46,156)( 47,157)
( 48,158)( 49,159)( 50,160)( 51,151)( 52,152)( 53,153)( 54,154)( 55,155)
( 56,161)( 57,162)( 58,163)( 59,164)( 60,165)( 61,216)( 62,217)( 63,218)
( 64,219)( 65,220)( 66,211)( 67,212)( 68,213)( 69,214)( 70,215)( 71,221)
( 72,222)( 73,223)( 74,224)( 75,225)( 76,231)( 77,232)( 78,233)( 79,234)
( 80,235)( 81,226)( 82,227)( 83,228)( 84,229)( 85,230)( 86,236)( 87,237)
( 88,238)( 89,239)( 90,240)( 91,186)( 92,187)( 93,188)( 94,189)( 95,190)
( 96,181)( 97,182)( 98,183)( 99,184)(100,185)(101,191)(102,192)(103,193)
(104,194)(105,195)(106,201)(107,202)(108,203)(109,204)(110,205)(111,196)
(112,197)(113,198)(114,199)(115,200)(116,206)(117,207)(118,208)(119,209)
(120,210);
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*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 >;
References : None.
to this polytope