Polytope of Type {2,8,30}

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

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

Permutation Representation (Magma) :

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

to this polytope