Polytope of Type {8,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,30}*960c
if this polytope has a name.
Group : SmallGroup(960,11105)
Rank : 3
Schlafli Type : {8,30}
Number of vertices, edges, etc : 16, 240, 60
Order of s₀s₁s₂ : 30
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {8,30,2} of size 1920
Vertex Figure Of :
   {2,8,30} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,30}*480
   4-fold quotients : {4,15}*240, {4,30}*240b, {4,30}*240c
   5-fold quotients : {8,6}*192c
   8-fold quotients : {4,15}*120, {2,30}*120
   10-fold quotients : {4,6}*96
   16-fold quotients : {2,15}*60
   20-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
   24-fold quotients : {2,10}*40
   40-fold quotients : {4,3}*24, {2,6}*24
   48-fold quotients : {2,5}*20
   80-fold quotients : {2,3}*12
   120-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,60}*1920f, {8,30}*1920f, {8,60}*1920g
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope