Polytope of Type {15,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15,10}*960
if this polytope has a name.
Group : SmallGroup(960,11364)
Rank : 3
Schlafli Type : {15,10}
Number of vertices, edges, etc : 48, 240, 32
Order of s0s1s2 : 12
Order of s0s1s2s1 : 10
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{15,10,2} of size 1920
Vertex Figure Of :
{2,15,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {5,10}*320b
6-fold quotients : {5,5}*160
80-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
2-fold covers : {15,20}*1920a, {15,20}*1920b, {15,10}*1920, {30,10}*1920a, {30,10}*1920b
Permutation Representation (GAP) :
s0 := ( 2, 11)( 3, 14)( 4, 8)( 6, 15)( 7, 10)( 9, 13)( 17, 65)( 18, 75)
( 19, 78)( 20, 72)( 21, 69)( 22, 79)( 23, 74)( 24, 68)( 25, 77)( 26, 71)
( 27, 66)( 28, 76)( 29, 73)( 30, 67)( 31, 70)( 32, 80)( 33, 49)( 34, 59)
( 35, 62)( 36, 56)( 37, 53)( 38, 63)( 39, 58)( 40, 52)( 41, 61)( 42, 55)
( 43, 50)( 44, 60)( 45, 57)( 46, 51)( 47, 54)( 48, 64)( 81,161)( 82,171)
( 83,174)( 84,168)( 85,165)( 86,175)( 87,170)( 88,164)( 89,173)( 90,167)
( 91,162)( 92,172)( 93,169)( 94,163)( 95,166)( 96,176)( 97,225)( 98,235)
( 99,238)(100,232)(101,229)(102,239)(103,234)(104,228)(105,237)(106,231)
(107,226)(108,236)(109,233)(110,227)(111,230)(112,240)(113,209)(114,219)
(115,222)(116,216)(117,213)(118,223)(119,218)(120,212)(121,221)(122,215)
(123,210)(124,220)(125,217)(126,211)(127,214)(128,224)(129,193)(130,203)
(131,206)(132,200)(133,197)(134,207)(135,202)(136,196)(137,205)(138,199)
(139,194)(140,204)(141,201)(142,195)(143,198)(144,208)(145,177)(146,187)
(147,190)(148,184)(149,181)(150,191)(151,186)(152,180)(153,189)(154,183)
(155,178)(156,188)(157,185)(158,179)(159,182)(160,192);;
s1 := ( 1, 97)( 2, 98)( 3,100)( 4, 99)( 5,102)( 6,101)( 7,103)( 8,104)
( 9,112)( 10,111)( 11,109)( 12,110)( 13,107)( 14,108)( 15,106)( 16,105)
( 17, 81)( 18, 82)( 19, 84)( 20, 83)( 21, 86)( 22, 85)( 23, 87)( 24, 88)
( 25, 96)( 26, 95)( 27, 93)( 28, 94)( 29, 91)( 30, 92)( 31, 90)( 32, 89)
( 33,145)( 34,146)( 35,148)( 36,147)( 37,150)( 38,149)( 39,151)( 40,152)
( 41,160)( 42,159)( 43,157)( 44,158)( 45,155)( 46,156)( 47,154)( 48,153)
( 49,129)( 50,130)( 51,132)( 52,131)( 53,134)( 54,133)( 55,135)( 56,136)
( 57,144)( 58,143)( 59,141)( 60,142)( 61,139)( 62,140)( 63,138)( 64,137)
( 65,113)( 66,114)( 67,116)( 68,115)( 69,118)( 70,117)( 71,119)( 72,120)
( 73,128)( 74,127)( 75,125)( 76,126)( 77,123)( 78,124)( 79,122)( 80,121)
(161,177)(162,178)(163,180)(164,179)(165,182)(166,181)(167,183)(168,184)
(169,192)(170,191)(171,189)(172,190)(173,187)(174,188)(175,186)(176,185)
(193,225)(194,226)(195,228)(196,227)(197,230)(198,229)(199,231)(200,232)
(201,240)(202,239)(203,237)(204,238)(205,235)(206,236)(207,234)(208,233)
(211,212)(213,214)(217,224)(218,223)(219,221)(220,222);;
s2 := ( 1, 5)( 2, 15)( 3, 10)( 6, 11)( 7, 14)( 12, 16)( 17, 69)( 18, 79)
( 19, 74)( 20, 68)( 21, 65)( 22, 75)( 23, 78)( 24, 72)( 25, 73)( 26, 67)
( 27, 70)( 28, 80)( 29, 77)( 30, 71)( 31, 66)( 32, 76)( 33, 53)( 34, 63)
( 35, 58)( 36, 52)( 37, 49)( 38, 59)( 39, 62)( 40, 56)( 41, 57)( 42, 51)
( 43, 54)( 44, 64)( 45, 61)( 46, 55)( 47, 50)( 48, 60)( 81, 85)( 82, 95)
( 83, 90)( 86, 91)( 87, 94)( 92, 96)( 97,149)( 98,159)( 99,154)(100,148)
(101,145)(102,155)(103,158)(104,152)(105,153)(106,147)(107,150)(108,160)
(109,157)(110,151)(111,146)(112,156)(113,133)(114,143)(115,138)(116,132)
(117,129)(118,139)(119,142)(120,136)(121,137)(122,131)(123,134)(124,144)
(125,141)(126,135)(127,130)(128,140)(161,165)(162,175)(163,170)(166,171)
(167,174)(172,176)(177,229)(178,239)(179,234)(180,228)(181,225)(182,235)
(183,238)(184,232)(185,233)(186,227)(187,230)(188,240)(189,237)(190,231)
(191,226)(192,236)(193,213)(194,223)(195,218)(196,212)(197,209)(198,219)
(199,222)(200,216)(201,217)(202,211)(203,214)(204,224)(205,221)(206,215)
(207,210)(208,220);;
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, s2*s0*s2*s0, s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1,
s0*s2*s1*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s2*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(240)!( 2, 11)( 3, 14)( 4, 8)( 6, 15)( 7, 10)( 9, 13)( 17, 65)
( 18, 75)( 19, 78)( 20, 72)( 21, 69)( 22, 79)( 23, 74)( 24, 68)( 25, 77)
( 26, 71)( 27, 66)( 28, 76)( 29, 73)( 30, 67)( 31, 70)( 32, 80)( 33, 49)
( 34, 59)( 35, 62)( 36, 56)( 37, 53)( 38, 63)( 39, 58)( 40, 52)( 41, 61)
( 42, 55)( 43, 50)( 44, 60)( 45, 57)( 46, 51)( 47, 54)( 48, 64)( 81,161)
( 82,171)( 83,174)( 84,168)( 85,165)( 86,175)( 87,170)( 88,164)( 89,173)
( 90,167)( 91,162)( 92,172)( 93,169)( 94,163)( 95,166)( 96,176)( 97,225)
( 98,235)( 99,238)(100,232)(101,229)(102,239)(103,234)(104,228)(105,237)
(106,231)(107,226)(108,236)(109,233)(110,227)(111,230)(112,240)(113,209)
(114,219)(115,222)(116,216)(117,213)(118,223)(119,218)(120,212)(121,221)
(122,215)(123,210)(124,220)(125,217)(126,211)(127,214)(128,224)(129,193)
(130,203)(131,206)(132,200)(133,197)(134,207)(135,202)(136,196)(137,205)
(138,199)(139,194)(140,204)(141,201)(142,195)(143,198)(144,208)(145,177)
(146,187)(147,190)(148,184)(149,181)(150,191)(151,186)(152,180)(153,189)
(154,183)(155,178)(156,188)(157,185)(158,179)(159,182)(160,192);
s1 := Sym(240)!( 1, 97)( 2, 98)( 3,100)( 4, 99)( 5,102)( 6,101)( 7,103)
( 8,104)( 9,112)( 10,111)( 11,109)( 12,110)( 13,107)( 14,108)( 15,106)
( 16,105)( 17, 81)( 18, 82)( 19, 84)( 20, 83)( 21, 86)( 22, 85)( 23, 87)
( 24, 88)( 25, 96)( 26, 95)( 27, 93)( 28, 94)( 29, 91)( 30, 92)( 31, 90)
( 32, 89)( 33,145)( 34,146)( 35,148)( 36,147)( 37,150)( 38,149)( 39,151)
( 40,152)( 41,160)( 42,159)( 43,157)( 44,158)( 45,155)( 46,156)( 47,154)
( 48,153)( 49,129)( 50,130)( 51,132)( 52,131)( 53,134)( 54,133)( 55,135)
( 56,136)( 57,144)( 58,143)( 59,141)( 60,142)( 61,139)( 62,140)( 63,138)
( 64,137)( 65,113)( 66,114)( 67,116)( 68,115)( 69,118)( 70,117)( 71,119)
( 72,120)( 73,128)( 74,127)( 75,125)( 76,126)( 77,123)( 78,124)( 79,122)
( 80,121)(161,177)(162,178)(163,180)(164,179)(165,182)(166,181)(167,183)
(168,184)(169,192)(170,191)(171,189)(172,190)(173,187)(174,188)(175,186)
(176,185)(193,225)(194,226)(195,228)(196,227)(197,230)(198,229)(199,231)
(200,232)(201,240)(202,239)(203,237)(204,238)(205,235)(206,236)(207,234)
(208,233)(211,212)(213,214)(217,224)(218,223)(219,221)(220,222);
s2 := Sym(240)!( 1, 5)( 2, 15)( 3, 10)( 6, 11)( 7, 14)( 12, 16)( 17, 69)
( 18, 79)( 19, 74)( 20, 68)( 21, 65)( 22, 75)( 23, 78)( 24, 72)( 25, 73)
( 26, 67)( 27, 70)( 28, 80)( 29, 77)( 30, 71)( 31, 66)( 32, 76)( 33, 53)
( 34, 63)( 35, 58)( 36, 52)( 37, 49)( 38, 59)( 39, 62)( 40, 56)( 41, 57)
( 42, 51)( 43, 54)( 44, 64)( 45, 61)( 46, 55)( 47, 50)( 48, 60)( 81, 85)
( 82, 95)( 83, 90)( 86, 91)( 87, 94)( 92, 96)( 97,149)( 98,159)( 99,154)
(100,148)(101,145)(102,155)(103,158)(104,152)(105,153)(106,147)(107,150)
(108,160)(109,157)(110,151)(111,146)(112,156)(113,133)(114,143)(115,138)
(116,132)(117,129)(118,139)(119,142)(120,136)(121,137)(122,131)(123,134)
(124,144)(125,141)(126,135)(127,130)(128,140)(161,165)(162,175)(163,170)
(166,171)(167,174)(172,176)(177,229)(178,239)(179,234)(180,228)(181,225)
(182,235)(183,238)(184,232)(185,233)(186,227)(187,230)(188,240)(189,237)
(190,231)(191,226)(192,236)(193,213)(194,223)(195,218)(196,212)(197,209)
(198,219)(199,222)(200,216)(201,217)(202,211)(203,214)(204,224)(205,221)
(206,215)(207,210)(208,220);
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,
s2*s0*s2*s0, s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1,
s0*s2*s1*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s2*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1 >;
References : None.
to this polytope