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# Polytope of Type {15,8}

Atlas Canonical Name : {15,8}*480
if this polytope has a name.
Group : SmallGroup(480,1032)
Rank : 3
Schlafli Type : {15,8}
Number of vertices, edges, etc : 30, 120, 16
Order of s0s1s2 : 60
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{15,8,2} of size 960
{15,8,4} of size 1920
Vertex Figure Of :
{2,15,8} of size 960
{4,15,8} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {15,4}*240
4-fold quotients : {15,4}*120
5-fold quotients : {3,8}*96
8-fold quotients : {15,2}*60
10-fold quotients : {3,4}*48
20-fold quotients : {3,4}*24
24-fold quotients : {5,2}*20
40-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
2-fold covers : {30,8}*960b
3-fold covers : {45,8}*1440, {15,24}*1440
4-fold covers : {15,8}*1920a, {60,8}*1920e, {30,8}*1920f, {60,8}*1920h
Permutation Representation (GAP) :
```s0 := (  3,  5)(  4,  6)(  7,  8)(  9, 33)( 10, 34)( 11, 37)( 12, 38)( 13, 35)
( 14, 36)( 15, 40)( 16, 39)( 17, 25)( 18, 26)( 19, 29)( 20, 30)( 21, 27)
( 22, 28)( 23, 32)( 24, 31)( 41, 81)( 42, 82)( 43, 85)( 44, 86)( 45, 83)
( 46, 84)( 47, 88)( 48, 87)( 49,113)( 50,114)( 51,117)( 52,118)( 53,115)
( 54,116)( 55,120)( 56,119)( 57,105)( 58,106)( 59,109)( 60,110)( 61,107)
( 62,108)( 63,112)( 64,111)( 65, 97)( 66, 98)( 67,101)( 68,102)( 69, 99)
( 70,100)( 71,104)( 72,103)( 73, 89)( 74, 90)( 75, 93)( 76, 94)( 77, 91)
( 78, 92)( 79, 96)( 80, 95)(121,122)(123,126)(124,125)(129,154)(130,153)
(131,158)(132,157)(133,156)(134,155)(135,159)(136,160)(137,146)(138,145)
(139,150)(140,149)(141,148)(142,147)(143,151)(144,152)(161,202)(162,201)
(163,206)(164,205)(165,204)(166,203)(167,207)(168,208)(169,234)(170,233)
(171,238)(172,237)(173,236)(174,235)(175,239)(176,240)(177,226)(178,225)
(179,230)(180,229)(181,228)(182,227)(183,231)(184,232)(185,218)(186,217)
(187,222)(188,221)(189,220)(190,219)(191,223)(192,224)(193,210)(194,209)
(195,214)(196,213)(197,212)(198,211)(199,215)(200,216);;
s1 := (  1, 49)(  2, 50)(  3, 52)(  4, 51)(  5, 55)(  6, 56)(  7, 53)(  8, 54)
(  9, 41)( 10, 42)( 11, 44)( 12, 43)( 13, 47)( 14, 48)( 15, 45)( 16, 46)
( 17, 73)( 18, 74)( 19, 76)( 20, 75)( 21, 79)( 22, 80)( 23, 77)( 24, 78)
( 25, 65)( 26, 66)( 27, 68)( 28, 67)( 29, 71)( 30, 72)( 31, 69)( 32, 70)
( 33, 57)( 34, 58)( 35, 60)( 36, 59)( 37, 63)( 38, 64)( 39, 61)( 40, 62)
( 81, 89)( 82, 90)( 83, 92)( 84, 91)( 85, 95)( 86, 96)( 87, 93)( 88, 94)
( 97,113)( 98,114)( 99,116)(100,115)(101,119)(102,120)(103,117)(104,118)
(107,108)(109,111)(110,112)(121,170)(122,169)(123,171)(124,172)(125,176)
(126,175)(127,174)(128,173)(129,162)(130,161)(131,163)(132,164)(133,168)
(134,167)(135,166)(136,165)(137,194)(138,193)(139,195)(140,196)(141,200)
(142,199)(143,198)(144,197)(145,186)(146,185)(147,187)(148,188)(149,192)
(150,191)(151,190)(152,189)(153,178)(154,177)(155,179)(156,180)(157,184)
(158,183)(159,182)(160,181)(201,210)(202,209)(203,211)(204,212)(205,216)
(206,215)(207,214)(208,213)(217,234)(218,233)(219,235)(220,236)(221,240)
(222,239)(223,238)(224,237)(225,226)(229,232)(230,231);;
s2 := (  1,127)(  2,128)(  3,125)(  4,126)(  5,124)(  6,123)(  7,122)(  8,121)
(  9,135)( 10,136)( 11,133)( 12,134)( 13,132)( 14,131)( 15,130)( 16,129)
( 17,143)( 18,144)( 19,141)( 20,142)( 21,140)( 22,139)( 23,138)( 24,137)
( 25,151)( 26,152)( 27,149)( 28,150)( 29,148)( 30,147)( 31,146)( 32,145)
( 33,159)( 34,160)( 35,157)( 36,158)( 37,156)( 38,155)( 39,154)( 40,153)
( 41,167)( 42,168)( 43,165)( 44,166)( 45,164)( 46,163)( 47,162)( 48,161)
( 49,175)( 50,176)( 51,173)( 52,174)( 53,172)( 54,171)( 55,170)( 56,169)
( 57,183)( 58,184)( 59,181)( 60,182)( 61,180)( 62,179)( 63,178)( 64,177)
( 65,191)( 66,192)( 67,189)( 68,190)( 69,188)( 70,187)( 71,186)( 72,185)
( 73,199)( 74,200)( 75,197)( 76,198)( 77,196)( 78,195)( 79,194)( 80,193)
( 81,207)( 82,208)( 83,205)( 84,206)( 85,204)( 86,203)( 87,202)( 88,201)
( 89,215)( 90,216)( 91,213)( 92,214)( 93,212)( 94,211)( 95,210)( 96,209)
( 97,223)( 98,224)( 99,221)(100,222)(101,220)(102,219)(103,218)(104,217)
(105,231)(106,232)(107,229)(108,230)(109,228)(110,227)(111,226)(112,225)
(113,239)(114,240)(115,237)(116,238)(117,236)(118,235)(119,234)(120,233);;
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*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*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 ];;
poly := F / rels;;

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

```
References : None.
to this polytope