Polytope of Type {2,10,12,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,12,3}*1920
if this polytope has a name.
Group : SmallGroup(1920,240195)
Rank : 5
Schlafli Type : {2,10,12,3}
Number of vertices, edges, etc : 2, 10, 80, 24, 4
Order of s0s1s2s3s4 : 40
Order of s0s1s2s3s4s3s2s1 : 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 : {2,10,6,3}*960
5-fold quotients : {2,2,12,3}*384
10-fold quotients : {2,2,6,3}*192
20-fold quotients : {2,2,3,3}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 11, 35)( 12, 36)( 13, 37)( 14, 38)( 15, 39)( 16, 40)( 17, 41)( 18, 42)
( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 25, 33)( 26, 34)
( 51, 75)( 52, 76)( 53, 77)( 54, 78)( 55, 79)( 56, 80)( 57, 81)( 58, 82)
( 59, 67)( 60, 68)( 61, 69)( 62, 70)( 63, 71)( 64, 72)( 65, 73)( 66, 74)
( 91,115)( 92,116)( 93,117)( 94,118)( 95,119)( 96,120)( 97,121)( 98,122)
( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)(105,113)(106,114)
(131,155)(132,156)(133,157)(134,158)(135,159)(136,160)(137,161)(138,162)
(139,147)(140,148)(141,149)(142,150)(143,151)(144,152)(145,153)(146,154)
(171,195)(172,196)(173,197)(174,198)(175,199)(176,200)(177,201)(178,202)
(179,187)(180,188)(181,189)(182,190)(183,191)(184,192)(185,193)(186,194)
(211,235)(212,236)(213,237)(214,238)(215,239)(216,240)(217,241)(218,242)
(219,227)(220,228)(221,229)(222,230)(223,231)(224,232)(225,233)(226,234);;
s2 := ( 3, 11)( 4, 12)( 5, 16)( 6, 15)( 7, 14)( 8, 13)( 9, 18)( 10, 17)
( 19, 35)( 20, 36)( 21, 40)( 22, 39)( 23, 38)( 24, 37)( 25, 42)( 26, 41)
( 29, 32)( 30, 31)( 33, 34)( 43, 91)( 44, 92)( 45, 96)( 46, 95)( 47, 94)
( 48, 93)( 49, 98)( 50, 97)( 51, 83)( 52, 84)( 53, 88)( 54, 87)( 55, 86)
( 56, 85)( 57, 90)( 58, 89)( 59,115)( 60,116)( 61,120)( 62,119)( 63,118)
( 64,117)( 65,122)( 66,121)( 67,107)( 68,108)( 69,112)( 70,111)( 71,110)
( 72,109)( 73,114)( 74,113)( 75, 99)( 76,100)( 77,104)( 78,103)( 79,102)
( 80,101)( 81,106)( 82,105)(123,132)(124,131)(125,135)(126,136)(127,133)
(128,134)(129,137)(130,138)(139,156)(140,155)(141,159)(142,160)(143,157)
(144,158)(145,161)(146,162)(147,148)(149,151)(150,152)(163,212)(164,211)
(165,215)(166,216)(167,213)(168,214)(169,217)(170,218)(171,204)(172,203)
(173,207)(174,208)(175,205)(176,206)(177,209)(178,210)(179,236)(180,235)
(181,239)(182,240)(183,237)(184,238)(185,241)(186,242)(187,228)(188,227)
(189,231)(190,232)(191,229)(192,230)(193,233)(194,234)(195,220)(196,219)
(197,223)(198,224)(199,221)(200,222)(201,225)(202,226);;
s3 := ( 3,163)( 4,164)( 5,166)( 6,165)( 7,169)( 8,170)( 9,167)( 10,168)
( 11,171)( 12,172)( 13,174)( 14,173)( 15,177)( 16,178)( 17,175)( 18,176)
( 19,179)( 20,180)( 21,182)( 22,181)( 23,185)( 24,186)( 25,183)( 26,184)
( 27,187)( 28,188)( 29,190)( 30,189)( 31,193)( 32,194)( 33,191)( 34,192)
( 35,195)( 36,196)( 37,198)( 38,197)( 39,201)( 40,202)( 41,199)( 42,200)
( 43,123)( 44,124)( 45,126)( 46,125)( 47,129)( 48,130)( 49,127)( 50,128)
( 51,131)( 52,132)( 53,134)( 54,133)( 55,137)( 56,138)( 57,135)( 58,136)
( 59,139)( 60,140)( 61,142)( 62,141)( 63,145)( 64,146)( 65,143)( 66,144)
( 67,147)( 68,148)( 69,150)( 70,149)( 71,153)( 72,154)( 73,151)( 74,152)
( 75,155)( 76,156)( 77,158)( 78,157)( 79,161)( 80,162)( 81,159)( 82,160)
( 83,203)( 84,204)( 85,206)( 86,205)( 87,209)( 88,210)( 89,207)( 90,208)
( 91,211)( 92,212)( 93,214)( 94,213)( 95,217)( 96,218)( 97,215)( 98,216)
( 99,219)(100,220)(101,222)(102,221)(103,225)(104,226)(105,223)(106,224)
(107,227)(108,228)(109,230)(110,229)(111,233)(112,234)(113,231)(114,232)
(115,235)(116,236)(117,238)(118,237)(119,241)(120,242)(121,239)(122,240);;
s4 := ( 3,130)( 4,129)( 5,126)( 6,125)( 7,127)( 8,128)( 9,124)( 10,123)
( 11,138)( 12,137)( 13,134)( 14,133)( 15,135)( 16,136)( 17,132)( 18,131)
( 19,146)( 20,145)( 21,142)( 22,141)( 23,143)( 24,144)( 25,140)( 26,139)
( 27,154)( 28,153)( 29,150)( 30,149)( 31,151)( 32,152)( 33,148)( 34,147)
( 35,162)( 36,161)( 37,158)( 38,157)( 39,159)( 40,160)( 41,156)( 42,155)
( 43,210)( 44,209)( 45,206)( 46,205)( 47,207)( 48,208)( 49,204)( 50,203)
( 51,218)( 52,217)( 53,214)( 54,213)( 55,215)( 56,216)( 57,212)( 58,211)
( 59,226)( 60,225)( 61,222)( 62,221)( 63,223)( 64,224)( 65,220)( 66,219)
( 67,234)( 68,233)( 69,230)( 70,229)( 71,231)( 72,232)( 73,228)( 74,227)
( 75,242)( 76,241)( 77,238)( 78,237)( 79,239)( 80,240)( 81,236)( 82,235)
( 83,170)( 84,169)( 85,166)( 86,165)( 87,167)( 88,168)( 89,164)( 90,163)
( 91,178)( 92,177)( 93,174)( 94,173)( 95,175)( 96,176)( 97,172)( 98,171)
( 99,186)(100,185)(101,182)(102,181)(103,183)(104,184)(105,180)(106,179)
(107,194)(108,193)(109,190)(110,189)(111,191)(112,192)(113,188)(114,187)
(115,202)(116,201)(117,198)(118,197)(119,199)(120,200)(121,196)(122,195);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*s2,
s4*s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3,
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)!( 11, 35)( 12, 36)( 13, 37)( 14, 38)( 15, 39)( 16, 40)( 17, 41)
( 18, 42)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 25, 33)
( 26, 34)( 51, 75)( 52, 76)( 53, 77)( 54, 78)( 55, 79)( 56, 80)( 57, 81)
( 58, 82)( 59, 67)( 60, 68)( 61, 69)( 62, 70)( 63, 71)( 64, 72)( 65, 73)
( 66, 74)( 91,115)( 92,116)( 93,117)( 94,118)( 95,119)( 96,120)( 97,121)
( 98,122)( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)(105,113)
(106,114)(131,155)(132,156)(133,157)(134,158)(135,159)(136,160)(137,161)
(138,162)(139,147)(140,148)(141,149)(142,150)(143,151)(144,152)(145,153)
(146,154)(171,195)(172,196)(173,197)(174,198)(175,199)(176,200)(177,201)
(178,202)(179,187)(180,188)(181,189)(182,190)(183,191)(184,192)(185,193)
(186,194)(211,235)(212,236)(213,237)(214,238)(215,239)(216,240)(217,241)
(218,242)(219,227)(220,228)(221,229)(222,230)(223,231)(224,232)(225,233)
(226,234);
s2 := Sym(242)!( 3, 11)( 4, 12)( 5, 16)( 6, 15)( 7, 14)( 8, 13)( 9, 18)
( 10, 17)( 19, 35)( 20, 36)( 21, 40)( 22, 39)( 23, 38)( 24, 37)( 25, 42)
( 26, 41)( 29, 32)( 30, 31)( 33, 34)( 43, 91)( 44, 92)( 45, 96)( 46, 95)
( 47, 94)( 48, 93)( 49, 98)( 50, 97)( 51, 83)( 52, 84)( 53, 88)( 54, 87)
( 55, 86)( 56, 85)( 57, 90)( 58, 89)( 59,115)( 60,116)( 61,120)( 62,119)
( 63,118)( 64,117)( 65,122)( 66,121)( 67,107)( 68,108)( 69,112)( 70,111)
( 71,110)( 72,109)( 73,114)( 74,113)( 75, 99)( 76,100)( 77,104)( 78,103)
( 79,102)( 80,101)( 81,106)( 82,105)(123,132)(124,131)(125,135)(126,136)
(127,133)(128,134)(129,137)(130,138)(139,156)(140,155)(141,159)(142,160)
(143,157)(144,158)(145,161)(146,162)(147,148)(149,151)(150,152)(163,212)
(164,211)(165,215)(166,216)(167,213)(168,214)(169,217)(170,218)(171,204)
(172,203)(173,207)(174,208)(175,205)(176,206)(177,209)(178,210)(179,236)
(180,235)(181,239)(182,240)(183,237)(184,238)(185,241)(186,242)(187,228)
(188,227)(189,231)(190,232)(191,229)(192,230)(193,233)(194,234)(195,220)
(196,219)(197,223)(198,224)(199,221)(200,222)(201,225)(202,226);
s3 := Sym(242)!( 3,163)( 4,164)( 5,166)( 6,165)( 7,169)( 8,170)( 9,167)
( 10,168)( 11,171)( 12,172)( 13,174)( 14,173)( 15,177)( 16,178)( 17,175)
( 18,176)( 19,179)( 20,180)( 21,182)( 22,181)( 23,185)( 24,186)( 25,183)
( 26,184)( 27,187)( 28,188)( 29,190)( 30,189)( 31,193)( 32,194)( 33,191)
( 34,192)( 35,195)( 36,196)( 37,198)( 38,197)( 39,201)( 40,202)( 41,199)
( 42,200)( 43,123)( 44,124)( 45,126)( 46,125)( 47,129)( 48,130)( 49,127)
( 50,128)( 51,131)( 52,132)( 53,134)( 54,133)( 55,137)( 56,138)( 57,135)
( 58,136)( 59,139)( 60,140)( 61,142)( 62,141)( 63,145)( 64,146)( 65,143)
( 66,144)( 67,147)( 68,148)( 69,150)( 70,149)( 71,153)( 72,154)( 73,151)
( 74,152)( 75,155)( 76,156)( 77,158)( 78,157)( 79,161)( 80,162)( 81,159)
( 82,160)( 83,203)( 84,204)( 85,206)( 86,205)( 87,209)( 88,210)( 89,207)
( 90,208)( 91,211)( 92,212)( 93,214)( 94,213)( 95,217)( 96,218)( 97,215)
( 98,216)( 99,219)(100,220)(101,222)(102,221)(103,225)(104,226)(105,223)
(106,224)(107,227)(108,228)(109,230)(110,229)(111,233)(112,234)(113,231)
(114,232)(115,235)(116,236)(117,238)(118,237)(119,241)(120,242)(121,239)
(122,240);
s4 := Sym(242)!( 3,130)( 4,129)( 5,126)( 6,125)( 7,127)( 8,128)( 9,124)
( 10,123)( 11,138)( 12,137)( 13,134)( 14,133)( 15,135)( 16,136)( 17,132)
( 18,131)( 19,146)( 20,145)( 21,142)( 22,141)( 23,143)( 24,144)( 25,140)
( 26,139)( 27,154)( 28,153)( 29,150)( 30,149)( 31,151)( 32,152)( 33,148)
( 34,147)( 35,162)( 36,161)( 37,158)( 38,157)( 39,159)( 40,160)( 41,156)
( 42,155)( 43,210)( 44,209)( 45,206)( 46,205)( 47,207)( 48,208)( 49,204)
( 50,203)( 51,218)( 52,217)( 53,214)( 54,213)( 55,215)( 56,216)( 57,212)
( 58,211)( 59,226)( 60,225)( 61,222)( 62,221)( 63,223)( 64,224)( 65,220)
( 66,219)( 67,234)( 68,233)( 69,230)( 70,229)( 71,231)( 72,232)( 73,228)
( 74,227)( 75,242)( 76,241)( 77,238)( 78,237)( 79,239)( 80,240)( 81,236)
( 82,235)( 83,170)( 84,169)( 85,166)( 86,165)( 87,167)( 88,168)( 89,164)
( 90,163)( 91,178)( 92,177)( 93,174)( 94,173)( 95,175)( 96,176)( 97,172)
( 98,171)( 99,186)(100,185)(101,182)(102,181)(103,183)(104,184)(105,180)
(106,179)(107,194)(108,193)(109,190)(110,189)(111,191)(112,192)(113,188)
(114,187)(115,202)(116,201)(117,198)(118,197)(119,199)(120,200)(121,196)
(122,195);
poly := sub<Sym(242)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4*s3*s4,
s1*s2*s3*s2*s1*s2*s3*s2, s4*s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope