Polytope of Type {2,60,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,60,6}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240195)
Rank : 4
Schlafli Type : {2,60,6}
Number of vertices, edges, etc : 2, 80, 240, 8
Order of s0s1s2s3 : 40
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 : {2,30,6}*960
4-fold quotients : {2,15,6}*480
5-fold quotients : {2,12,6}*384b
10-fold quotients : {2,12,3}*192, {2,6,6}*192
20-fold quotients : {2,3,6}*96, {2,6,3}*96
24-fold quotients : {2,10,2}*80
40-fold quotients : {2,3,3}*48
48-fold quotients : {2,5,2}*40
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 := ( 3,171)( 4,172)( 5,174)( 6,173)( 7,177)( 8,178)( 9,175)( 10,176)
( 11,163)( 12,164)( 13,166)( 14,165)( 15,169)( 16,170)( 17,167)( 18,168)
( 19,195)( 20,196)( 21,198)( 22,197)( 23,201)( 24,202)( 25,199)( 26,200)
( 27,187)( 28,188)( 29,190)( 30,189)( 31,193)( 32,194)( 33,191)( 34,192)
( 35,179)( 36,180)( 37,182)( 38,181)( 39,185)( 40,186)( 41,183)( 42,184)
( 43,131)( 44,132)( 45,134)( 46,133)( 47,137)( 48,138)( 49,135)( 50,136)
( 51,123)( 52,124)( 53,126)( 54,125)( 55,129)( 56,130)( 57,127)( 58,128)
( 59,155)( 60,156)( 61,158)( 62,157)( 63,161)( 64,162)( 65,159)( 66,160)
( 67,147)( 68,148)( 69,150)( 70,149)( 71,153)( 72,154)( 73,151)( 74,152)
( 75,139)( 76,140)( 77,142)( 78,141)( 79,145)( 80,146)( 81,143)( 82,144)
( 83,211)( 84,212)( 85,214)( 86,213)( 87,217)( 88,218)( 89,215)( 90,216)
( 91,203)( 92,204)( 93,206)( 94,205)( 95,209)( 96,210)( 97,207)( 98,208)
( 99,235)(100,236)(101,238)(102,237)(103,241)(104,242)(105,239)(106,240)
(107,227)(108,228)(109,230)(110,229)(111,233)(112,234)(113,231)(114,232)
(115,219)(116,220)(117,222)(118,221)(119,225)(120,226)(121,223)(122,224);;
s3 := ( 3,129)( 4,130)( 5,125)( 6,126)( 7,128)( 8,127)( 9,123)( 10,124)
( 11,137)( 12,138)( 13,133)( 14,134)( 15,136)( 16,135)( 17,131)( 18,132)
( 19,145)( 20,146)( 21,141)( 22,142)( 23,144)( 24,143)( 25,139)( 26,140)
( 27,153)( 28,154)( 29,149)( 30,150)( 31,152)( 32,151)( 33,147)( 34,148)
( 35,161)( 36,162)( 37,157)( 38,158)( 39,160)( 40,159)( 41,155)( 42,156)
( 43,209)( 44,210)( 45,205)( 46,206)( 47,208)( 48,207)( 49,203)( 50,204)
( 51,217)( 52,218)( 53,213)( 54,214)( 55,216)( 56,215)( 57,211)( 58,212)
( 59,225)( 60,226)( 61,221)( 62,222)( 63,224)( 64,223)( 65,219)( 66,220)
( 67,233)( 68,234)( 69,229)( 70,230)( 71,232)( 72,231)( 73,227)( 74,228)
( 75,241)( 76,242)( 77,237)( 78,238)( 79,240)( 80,239)( 81,235)( 82,236)
( 83,169)( 84,170)( 85,165)( 86,166)( 87,168)( 88,167)( 89,163)( 90,164)
( 91,177)( 92,178)( 93,173)( 94,174)( 95,176)( 96,175)( 97,171)( 98,172)
( 99,185)(100,186)(101,181)(102,182)(103,184)(104,183)(105,179)(106,180)
(107,193)(108,194)(109,189)(110,190)(111,192)(112,191)(113,187)(114,188)
(115,201)(116,202)(117,197)(118,198)(119,200)(120,199)(121,195)(122,196);;
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,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s3*s2*s1*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2*s1*s2,
s3*s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2,
s1*s2*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s1*s3*s2*s1*s3*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)!( 3,171)( 4,172)( 5,174)( 6,173)( 7,177)( 8,178)( 9,175)
( 10,176)( 11,163)( 12,164)( 13,166)( 14,165)( 15,169)( 16,170)( 17,167)
( 18,168)( 19,195)( 20,196)( 21,198)( 22,197)( 23,201)( 24,202)( 25,199)
( 26,200)( 27,187)( 28,188)( 29,190)( 30,189)( 31,193)( 32,194)( 33,191)
( 34,192)( 35,179)( 36,180)( 37,182)( 38,181)( 39,185)( 40,186)( 41,183)
( 42,184)( 43,131)( 44,132)( 45,134)( 46,133)( 47,137)( 48,138)( 49,135)
( 50,136)( 51,123)( 52,124)( 53,126)( 54,125)( 55,129)( 56,130)( 57,127)
( 58,128)( 59,155)( 60,156)( 61,158)( 62,157)( 63,161)( 64,162)( 65,159)
( 66,160)( 67,147)( 68,148)( 69,150)( 70,149)( 71,153)( 72,154)( 73,151)
( 74,152)( 75,139)( 76,140)( 77,142)( 78,141)( 79,145)( 80,146)( 81,143)
( 82,144)( 83,211)( 84,212)( 85,214)( 86,213)( 87,217)( 88,218)( 89,215)
( 90,216)( 91,203)( 92,204)( 93,206)( 94,205)( 95,209)( 96,210)( 97,207)
( 98,208)( 99,235)(100,236)(101,238)(102,237)(103,241)(104,242)(105,239)
(106,240)(107,227)(108,228)(109,230)(110,229)(111,233)(112,234)(113,231)
(114,232)(115,219)(116,220)(117,222)(118,221)(119,225)(120,226)(121,223)
(122,224);
s3 := Sym(242)!( 3,129)( 4,130)( 5,125)( 6,126)( 7,128)( 8,127)( 9,123)
( 10,124)( 11,137)( 12,138)( 13,133)( 14,134)( 15,136)( 16,135)( 17,131)
( 18,132)( 19,145)( 20,146)( 21,141)( 22,142)( 23,144)( 24,143)( 25,139)
( 26,140)( 27,153)( 28,154)( 29,149)( 30,150)( 31,152)( 32,151)( 33,147)
( 34,148)( 35,161)( 36,162)( 37,157)( 38,158)( 39,160)( 40,159)( 41,155)
( 42,156)( 43,209)( 44,210)( 45,205)( 46,206)( 47,208)( 48,207)( 49,203)
( 50,204)( 51,217)( 52,218)( 53,213)( 54,214)( 55,216)( 56,215)( 57,211)
( 58,212)( 59,225)( 60,226)( 61,221)( 62,222)( 63,224)( 64,223)( 65,219)
( 66,220)( 67,233)( 68,234)( 69,229)( 70,230)( 71,232)( 72,231)( 73,227)
( 74,228)( 75,241)( 76,242)( 77,237)( 78,238)( 79,240)( 80,239)( 81,235)
( 82,236)( 83,169)( 84,170)( 85,165)( 86,166)( 87,168)( 88,167)( 89,163)
( 90,164)( 91,177)( 92,178)( 93,173)( 94,174)( 95,176)( 96,175)( 97,171)
( 98,172)( 99,185)(100,186)(101,181)(102,182)(103,184)(104,183)(105,179)
(106,180)(107,193)(108,194)(109,189)(110,190)(111,192)(112,191)(113,187)
(114,188)(115,201)(116,202)(117,197)(118,198)(119,200)(120,199)(121,195)
(122,196);
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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s3*s2*s1*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2*s1*s2,
s3*s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2,
s1*s2*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s1*s3*s2*s1*s3*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope