Polytope of Type {2,12,40}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,40}*1920a
if this polytope has a name.
Group : SmallGroup(1920,148921)
Rank : 4
Schlafli Type : {2,12,40}
Number of vertices, edges, etc : 2, 12, 240, 40
Order of s₀s₁s₂s₃ : 120
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 : {2,6,40}*960, {2,12,20}*960
   3-fold quotients : {2,4,40}*640a
   4-fold quotients : {2,12,10}*480, {2,6,20}*480a
   5-fold quotients : {2,12,8}*384a
   6-fold quotients : {2,4,20}*320, {2,2,40}*320
   8-fold quotients : {2,6,10}*240
   10-fold quotients : {2,12,4}*192a, {2,6,8}*192
   12-fold quotients : {2,2,20}*160, {2,4,10}*160
   15-fold quotients : {2,4,8}*128a
   20-fold quotients : {2,12,2}*96, {2,6,4}*96a
   24-fold quotients : {2,2,10}*80
   30-fold quotients : {2,4,4}*64, {2,2,8}*64
   40-fold quotients : {2,6,2}*48
   48-fold quotients : {2,2,5}*40
   60-fold quotients : {2,2,4}*32, {2,4,2}*32
   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 := (  8, 13)(  9, 14)( 10, 15)( 11, 16)( 12, 17)( 23, 28)( 24, 29)( 25, 30)
( 26, 31)( 27, 32)( 38, 43)( 39, 44)( 40, 45)( 41, 46)( 42, 47)( 53, 58)
( 54, 59)( 55, 60)( 56, 61)( 57, 62)( 68, 73)( 69, 74)( 70, 75)( 71, 76)
( 72, 77)( 83, 88)( 84, 89)( 85, 90)( 86, 91)( 87, 92)( 98,103)( 99,104)
(100,105)(101,106)(102,107)(113,118)(114,119)(115,120)(116,121)(117,122)
(123,153)(124,154)(125,155)(126,156)(127,157)(128,163)(129,164)(130,165)
(131,166)(132,167)(133,158)(134,159)(135,160)(136,161)(137,162)(138,168)
(139,169)(140,170)(141,171)(142,172)(143,178)(144,179)(145,180)(146,181)
(147,182)(148,173)(149,174)(150,175)(151,176)(152,177)(183,213)(184,214)
(185,215)(186,216)(187,217)(188,223)(189,224)(190,225)(191,226)(192,227)
(193,218)(194,219)(195,220)(196,221)(197,222)(198,228)(199,229)(200,230)
(201,231)(202,232)(203,238)(204,239)(205,240)(206,241)(207,242)(208,233)
(209,234)(210,235)(211,236)(212,237);;
s2 := (  3,128)(  4,132)(  5,131)(  6,130)(  7,129)(  8,123)(  9,127)( 10,126)
( 11,125)( 12,124)( 13,133)( 14,137)( 15,136)( 16,135)( 17,134)( 18,143)
( 19,147)( 20,146)( 21,145)( 22,144)( 23,138)( 24,142)( 25,141)( 26,140)
( 27,139)( 28,148)( 29,152)( 30,151)( 31,150)( 32,149)( 33,158)( 34,162)
( 35,161)( 36,160)( 37,159)( 38,153)( 39,157)( 40,156)( 41,155)( 42,154)
( 43,163)( 44,167)( 45,166)( 46,165)( 47,164)( 48,173)( 49,177)( 50,176)
( 51,175)( 52,174)( 53,168)( 54,172)( 55,171)( 56,170)( 57,169)( 58,178)
( 59,182)( 60,181)( 61,180)( 62,179)( 63,203)( 64,207)( 65,206)( 66,205)
( 67,204)( 68,198)( 69,202)( 70,201)( 71,200)( 72,199)( 73,208)( 74,212)
( 75,211)( 76,210)( 77,209)( 78,188)( 79,192)( 80,191)( 81,190)( 82,189)
( 83,183)( 84,187)( 85,186)( 86,185)( 87,184)( 88,193)( 89,197)( 90,196)
( 91,195)( 92,194)( 93,233)( 94,237)( 95,236)( 96,235)( 97,234)( 98,228)
( 99,232)(100,231)(101,230)(102,229)(103,238)(104,242)(105,241)(106,240)
(107,239)(108,218)(109,222)(110,221)(111,220)(112,219)(113,213)(114,217)
(115,216)(116,215)(117,214)(118,223)(119,227)(120,226)(121,225)(122,224);;
s3 := (  3,  4)(  5,  7)(  8,  9)( 10, 12)( 13, 14)( 15, 17)( 18, 19)( 20, 22)
( 23, 24)( 25, 27)( 28, 29)( 30, 32)( 33, 34)( 35, 37)( 38, 39)( 40, 42)
( 43, 44)( 45, 47)( 48, 49)( 50, 52)( 53, 54)( 55, 57)( 58, 59)( 60, 62)
( 63, 79)( 64, 78)( 65, 82)( 66, 81)( 67, 80)( 68, 84)( 69, 83)( 70, 87)
( 71, 86)( 72, 85)( 73, 89)( 74, 88)( 75, 92)( 76, 91)( 77, 90)( 93,109)
( 94,108)( 95,112)( 96,111)( 97,110)( 98,114)( 99,113)(100,117)(101,116)
(102,115)(103,119)(104,118)(105,122)(106,121)(107,120)(123,184)(124,183)
(125,187)(126,186)(127,185)(128,189)(129,188)(130,192)(131,191)(132,190)
(133,194)(134,193)(135,197)(136,196)(137,195)(138,199)(139,198)(140,202)
(141,201)(142,200)(143,204)(144,203)(145,207)(146,206)(147,205)(148,209)
(149,208)(150,212)(151,211)(152,210)(153,214)(154,213)(155,217)(156,216)
(157,215)(158,219)(159,218)(160,222)(161,221)(162,220)(163,224)(164,223)
(165,227)(166,226)(167,225)(168,229)(169,228)(170,232)(171,231)(172,230)
(173,234)(174,233)(175,237)(176,236)(177,235)(178,239)(179,238)(180,242)
(181,241)(182,240);;
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, 
s1*s2*s3*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, 
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*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)!(  8, 13)(  9, 14)( 10, 15)( 11, 16)( 12, 17)( 23, 28)( 24, 29)
( 25, 30)( 26, 31)( 27, 32)( 38, 43)( 39, 44)( 40, 45)( 41, 46)( 42, 47)
( 53, 58)( 54, 59)( 55, 60)( 56, 61)( 57, 62)( 68, 73)( 69, 74)( 70, 75)
( 71, 76)( 72, 77)( 83, 88)( 84, 89)( 85, 90)( 86, 91)( 87, 92)( 98,103)
( 99,104)(100,105)(101,106)(102,107)(113,118)(114,119)(115,120)(116,121)
(117,122)(123,153)(124,154)(125,155)(126,156)(127,157)(128,163)(129,164)
(130,165)(131,166)(132,167)(133,158)(134,159)(135,160)(136,161)(137,162)
(138,168)(139,169)(140,170)(141,171)(142,172)(143,178)(144,179)(145,180)
(146,181)(147,182)(148,173)(149,174)(150,175)(151,176)(152,177)(183,213)
(184,214)(185,215)(186,216)(187,217)(188,223)(189,224)(190,225)(191,226)
(192,227)(193,218)(194,219)(195,220)(196,221)(197,222)(198,228)(199,229)
(200,230)(201,231)(202,232)(203,238)(204,239)(205,240)(206,241)(207,242)
(208,233)(209,234)(210,235)(211,236)(212,237);
s2 := Sym(242)!(  3,128)(  4,132)(  5,131)(  6,130)(  7,129)(  8,123)(  9,127)
( 10,126)( 11,125)( 12,124)( 13,133)( 14,137)( 15,136)( 16,135)( 17,134)
( 18,143)( 19,147)( 20,146)( 21,145)( 22,144)( 23,138)( 24,142)( 25,141)
( 26,140)( 27,139)( 28,148)( 29,152)( 30,151)( 31,150)( 32,149)( 33,158)
( 34,162)( 35,161)( 36,160)( 37,159)( 38,153)( 39,157)( 40,156)( 41,155)
( 42,154)( 43,163)( 44,167)( 45,166)( 46,165)( 47,164)( 48,173)( 49,177)
( 50,176)( 51,175)( 52,174)( 53,168)( 54,172)( 55,171)( 56,170)( 57,169)
( 58,178)( 59,182)( 60,181)( 61,180)( 62,179)( 63,203)( 64,207)( 65,206)
( 66,205)( 67,204)( 68,198)( 69,202)( 70,201)( 71,200)( 72,199)( 73,208)
( 74,212)( 75,211)( 76,210)( 77,209)( 78,188)( 79,192)( 80,191)( 81,190)
( 82,189)( 83,183)( 84,187)( 85,186)( 86,185)( 87,184)( 88,193)( 89,197)
( 90,196)( 91,195)( 92,194)( 93,233)( 94,237)( 95,236)( 96,235)( 97,234)
( 98,228)( 99,232)(100,231)(101,230)(102,229)(103,238)(104,242)(105,241)
(106,240)(107,239)(108,218)(109,222)(110,221)(111,220)(112,219)(113,213)
(114,217)(115,216)(116,215)(117,214)(118,223)(119,227)(120,226)(121,225)
(122,224);
s3 := Sym(242)!(  3,  4)(  5,  7)(  8,  9)( 10, 12)( 13, 14)( 15, 17)( 18, 19)
( 20, 22)( 23, 24)( 25, 27)( 28, 29)( 30, 32)( 33, 34)( 35, 37)( 38, 39)
( 40, 42)( 43, 44)( 45, 47)( 48, 49)( 50, 52)( 53, 54)( 55, 57)( 58, 59)
( 60, 62)( 63, 79)( 64, 78)( 65, 82)( 66, 81)( 67, 80)( 68, 84)( 69, 83)
( 70, 87)( 71, 86)( 72, 85)( 73, 89)( 74, 88)( 75, 92)( 76, 91)( 77, 90)
( 93,109)( 94,108)( 95,112)( 96,111)( 97,110)( 98,114)( 99,113)(100,117)
(101,116)(102,115)(103,119)(104,118)(105,122)(106,121)(107,120)(123,184)
(124,183)(125,187)(126,186)(127,185)(128,189)(129,188)(130,192)(131,191)
(132,190)(133,194)(134,193)(135,197)(136,196)(137,195)(138,199)(139,198)
(140,202)(141,201)(142,200)(143,204)(144,203)(145,207)(146,206)(147,205)
(148,209)(149,208)(150,212)(151,211)(152,210)(153,214)(154,213)(155,217)
(156,216)(157,215)(158,219)(159,218)(160,222)(161,221)(162,220)(163,224)
(164,223)(165,227)(166,226)(167,225)(168,229)(169,228)(170,232)(171,231)
(172,230)(173,234)(174,233)(175,237)(176,236)(177,235)(178,239)(179,238)
(180,242)(181,241)(182,240);
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, s1*s2*s3*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, 
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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope