Polytope of Type {2,30,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,30,8}*1920c
if this polytope has a name.
Group : SmallGroup(1920,240310)
Rank : 4
Schlafli Type : {2,30,8}
Number of vertices, edges, etc : 2, 60, 240, 16
Order of s₀s₁s₂s₃ : 30
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,30,4}*960
   4-fold quotients : {2,15,4}*480, {2,30,4}*480b, {2,30,4}*480c
   5-fold quotients : {2,6,8}*384c
   8-fold quotients : {2,15,4}*240, {2,30,2}*240
   10-fold quotients : {2,6,4}*192
   16-fold quotients : {2,15,2}*120
   20-fold quotients : {2,3,4}*96, {2,6,4}*96b, {2,6,4}*96c
   24-fold quotients : {2,10,2}*80
   40-fold quotients : {2,3,4}*48, {2,6,2}*48
   48-fold quotients : {2,5,2}*40
   80-fold quotients : {2,3,2}*24
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  5,  8)(  6,  7)(  9, 10)( 11, 35)( 12, 36)( 13, 40)( 14, 39)( 15, 38)
( 16, 37)( 17, 42)( 18, 41)( 19, 27)( 20, 28)( 21, 32)( 22, 31)( 23, 30)
( 24, 29)( 25, 34)( 26, 33)( 43, 83)( 44, 84)( 45, 88)( 46, 87)( 47, 86)
( 48, 85)( 49, 90)( 50, 89)( 51,115)( 52,116)( 53,120)( 54,119)( 55,118)
( 56,117)( 57,122)( 58,121)( 59,107)( 60,108)( 61,112)( 62,111)( 63,110)
( 64,109)( 65,114)( 66,113)( 67, 99)( 68,100)( 69,104)( 70,103)( 71,102)
( 72,101)( 73,106)( 74,105)( 75, 91)( 76, 92)( 77, 96)( 78, 95)( 79, 94)
( 80, 93)( 81, 98)( 82, 97)(123,124)(125,127)(126,128)(131,156)(132,155)
(133,159)(134,160)(135,157)(136,158)(137,161)(138,162)(139,148)(140,147)
(141,151)(142,152)(143,149)(144,150)(145,153)(146,154)(163,204)(164,203)
(165,207)(166,208)(167,205)(168,206)(169,209)(170,210)(171,236)(172,235)
(173,239)(174,240)(175,237)(176,238)(177,241)(178,242)(179,228)(180,227)
(181,231)(182,232)(183,229)(184,230)(185,233)(186,234)(187,220)(188,219)
(189,223)(190,224)(191,221)(192,222)(193,225)(194,226)(195,212)(196,211)
(197,215)(198,216)(199,213)(200,214)(201,217)(202,218);;
s2 := (  3, 51)(  4, 52)(  5, 54)(  6, 53)(  7, 57)(  8, 58)(  9, 55)( 10, 56)
( 11, 43)( 12, 44)( 13, 46)( 14, 45)( 15, 49)( 16, 50)( 17, 47)( 18, 48)
( 19, 75)( 20, 76)( 21, 78)( 22, 77)( 23, 81)( 24, 82)( 25, 79)( 26, 80)
( 27, 67)( 28, 68)( 29, 70)( 30, 69)( 31, 73)( 32, 74)( 33, 71)( 34, 72)
( 35, 59)( 36, 60)( 37, 62)( 38, 61)( 39, 65)( 40, 66)( 41, 63)( 42, 64)
( 83, 91)( 84, 92)( 85, 94)( 86, 93)( 87, 97)( 88, 98)( 89, 95)( 90, 96)
( 99,115)(100,116)(101,118)(102,117)(103,121)(104,122)(105,119)(106,120)
(109,110)(111,113)(112,114)(123,171)(124,172)(125,174)(126,173)(127,177)
(128,178)(129,175)(130,176)(131,163)(132,164)(133,166)(134,165)(135,169)
(136,170)(137,167)(138,168)(139,195)(140,196)(141,198)(142,197)(143,201)
(144,202)(145,199)(146,200)(147,187)(148,188)(149,190)(150,189)(151,193)
(152,194)(153,191)(154,192)(155,179)(156,180)(157,182)(158,181)(159,185)
(160,186)(161,183)(162,184)(203,211)(204,212)(205,214)(206,213)(207,217)
(208,218)(209,215)(210,216)(219,235)(220,236)(221,238)(222,237)(223,241)
(224,242)(225,239)(226,240)(229,230)(231,233)(232,234);;
s3 := (  3,129)(  4,130)(  5,127)(  6,128)(  7,126)(  8,125)(  9,124)( 10,123)
( 11,137)( 12,138)( 13,135)( 14,136)( 15,134)( 16,133)( 17,132)( 18,131)
( 19,145)( 20,146)( 21,143)( 22,144)( 23,142)( 24,141)( 25,140)( 26,139)
( 27,153)( 28,154)( 29,151)( 30,152)( 31,150)( 32,149)( 33,148)( 34,147)
( 35,161)( 36,162)( 37,159)( 38,160)( 39,158)( 40,157)( 41,156)( 42,155)
( 43,169)( 44,170)( 45,167)( 46,168)( 47,166)( 48,165)( 49,164)( 50,163)
( 51,177)( 52,178)( 53,175)( 54,176)( 55,174)( 56,173)( 57,172)( 58,171)
( 59,185)( 60,186)( 61,183)( 62,184)( 63,182)( 64,181)( 65,180)( 66,179)
( 67,193)( 68,194)( 69,191)( 70,192)( 71,190)( 72,189)( 73,188)( 74,187)
( 75,201)( 76,202)( 77,199)( 78,200)( 79,198)( 80,197)( 81,196)( 82,195)
( 83,209)( 84,210)( 85,207)( 86,208)( 87,206)( 88,205)( 89,204)( 90,203)
( 91,217)( 92,218)( 93,215)( 94,216)( 95,214)( 96,213)( 97,212)( 98,211)
( 99,225)(100,226)(101,223)(102,224)(103,222)(104,221)(105,220)(106,219)
(107,233)(108,234)(109,231)(110,232)(111,230)(112,229)(113,228)(114,227)
(115,241)(116,242)(117,239)(118,240)(119,238)(120,237)(121,236)(122,235);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*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(242)!(1,2);
s1 := Sym(242)!(  5,  8)(  6,  7)(  9, 10)( 11, 35)( 12, 36)( 13, 40)( 14, 39)
( 15, 38)( 16, 37)( 17, 42)( 18, 41)( 19, 27)( 20, 28)( 21, 32)( 22, 31)
( 23, 30)( 24, 29)( 25, 34)( 26, 33)( 43, 83)( 44, 84)( 45, 88)( 46, 87)
( 47, 86)( 48, 85)( 49, 90)( 50, 89)( 51,115)( 52,116)( 53,120)( 54,119)
( 55,118)( 56,117)( 57,122)( 58,121)( 59,107)( 60,108)( 61,112)( 62,111)
( 63,110)( 64,109)( 65,114)( 66,113)( 67, 99)( 68,100)( 69,104)( 70,103)
( 71,102)( 72,101)( 73,106)( 74,105)( 75, 91)( 76, 92)( 77, 96)( 78, 95)
( 79, 94)( 80, 93)( 81, 98)( 82, 97)(123,124)(125,127)(126,128)(131,156)
(132,155)(133,159)(134,160)(135,157)(136,158)(137,161)(138,162)(139,148)
(140,147)(141,151)(142,152)(143,149)(144,150)(145,153)(146,154)(163,204)
(164,203)(165,207)(166,208)(167,205)(168,206)(169,209)(170,210)(171,236)
(172,235)(173,239)(174,240)(175,237)(176,238)(177,241)(178,242)(179,228)
(180,227)(181,231)(182,232)(183,229)(184,230)(185,233)(186,234)(187,220)
(188,219)(189,223)(190,224)(191,221)(192,222)(193,225)(194,226)(195,212)
(196,211)(197,215)(198,216)(199,213)(200,214)(201,217)(202,218);
s2 := Sym(242)!(  3, 51)(  4, 52)(  5, 54)(  6, 53)(  7, 57)(  8, 58)(  9, 55)
( 10, 56)( 11, 43)( 12, 44)( 13, 46)( 14, 45)( 15, 49)( 16, 50)( 17, 47)
( 18, 48)( 19, 75)( 20, 76)( 21, 78)( 22, 77)( 23, 81)( 24, 82)( 25, 79)
( 26, 80)( 27, 67)( 28, 68)( 29, 70)( 30, 69)( 31, 73)( 32, 74)( 33, 71)
( 34, 72)( 35, 59)( 36, 60)( 37, 62)( 38, 61)( 39, 65)( 40, 66)( 41, 63)
( 42, 64)( 83, 91)( 84, 92)( 85, 94)( 86, 93)( 87, 97)( 88, 98)( 89, 95)
( 90, 96)( 99,115)(100,116)(101,118)(102,117)(103,121)(104,122)(105,119)
(106,120)(109,110)(111,113)(112,114)(123,171)(124,172)(125,174)(126,173)
(127,177)(128,178)(129,175)(130,176)(131,163)(132,164)(133,166)(134,165)
(135,169)(136,170)(137,167)(138,168)(139,195)(140,196)(141,198)(142,197)
(143,201)(144,202)(145,199)(146,200)(147,187)(148,188)(149,190)(150,189)
(151,193)(152,194)(153,191)(154,192)(155,179)(156,180)(157,182)(158,181)
(159,185)(160,186)(161,183)(162,184)(203,211)(204,212)(205,214)(206,213)
(207,217)(208,218)(209,215)(210,216)(219,235)(220,236)(221,238)(222,237)
(223,241)(224,242)(225,239)(226,240)(229,230)(231,233)(232,234);
s3 := Sym(242)!(  3,129)(  4,130)(  5,127)(  6,128)(  7,126)(  8,125)(  9,124)
( 10,123)( 11,137)( 12,138)( 13,135)( 14,136)( 15,134)( 16,133)( 17,132)
( 18,131)( 19,145)( 20,146)( 21,143)( 22,144)( 23,142)( 24,141)( 25,140)
( 26,139)( 27,153)( 28,154)( 29,151)( 30,152)( 31,150)( 32,149)( 33,148)
( 34,147)( 35,161)( 36,162)( 37,159)( 38,160)( 39,158)( 40,157)( 41,156)
( 42,155)( 43,169)( 44,170)( 45,167)( 46,168)( 47,166)( 48,165)( 49,164)
( 50,163)( 51,177)( 52,178)( 53,175)( 54,176)( 55,174)( 56,173)( 57,172)
( 58,171)( 59,185)( 60,186)( 61,183)( 62,184)( 63,182)( 64,181)( 65,180)
( 66,179)( 67,193)( 68,194)( 69,191)( 70,192)( 71,190)( 72,189)( 73,188)
( 74,187)( 75,201)( 76,202)( 77,199)( 78,200)( 79,198)( 80,197)( 81,196)
( 82,195)( 83,209)( 84,210)( 85,207)( 86,208)( 87,206)( 88,205)( 89,204)
( 90,203)( 91,217)( 92,218)( 93,215)( 94,216)( 95,214)( 96,213)( 97,212)
( 98,211)( 99,225)(100,226)(101,223)(102,224)(103,222)(104,221)(105,220)
(106,219)(107,233)(108,234)(109,231)(110,232)(111,230)(112,229)(113,228)
(114,227)(115,241)(116,242)(117,239)(118,240)(119,238)(120,237)(121,236)
(122,235);
poly := sub<Sym(242)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s3*s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*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 >;

to this polytope