Polytope of Type {10,12,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,12,3}*960
if this polytope has a name.
Group : SmallGroup(960,10979)
Rank : 4
Schlafli Type : {10,12,3}
Number of vertices, edges, etc : 10, 80, 24, 4
Order of s0s1s2s3 : 40
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{10,12,3,2} of size 1920
Vertex Figure Of :
{2,10,12,3} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {10,6,3}*480
5-fold quotients : {2,12,3}*192
10-fold quotients : {2,6,3}*96
20-fold quotients : {2,3,3}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {20,12,3}*1920, {10,12,6}*1920b
Permutation Representation (GAP) :
s0 := ( 9, 33)( 10, 34)( 11, 35)( 12, 36)( 13, 37)( 14, 38)( 15, 39)( 16, 40)
( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)
( 49, 73)( 50, 74)( 51, 75)( 52, 76)( 53, 77)( 54, 78)( 55, 79)( 56, 80)
( 57, 65)( 58, 66)( 59, 67)( 60, 68)( 61, 69)( 62, 70)( 63, 71)( 64, 72)
( 89,113)( 90,114)( 91,115)( 92,116)( 93,117)( 94,118)( 95,119)( 96,120)
( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)
(129,153)(130,154)(131,155)(132,156)(133,157)(134,158)(135,159)(136,160)
(137,145)(138,146)(139,147)(140,148)(141,149)(142,150)(143,151)(144,152)
(169,193)(170,194)(171,195)(172,196)(173,197)(174,198)(175,199)(176,200)
(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)(184,192)
(209,233)(210,234)(211,235)(212,236)(213,237)(214,238)(215,239)(216,240)
(217,225)(218,226)(219,227)(220,228)(221,229)(222,230)(223,231)(224,232);;
s1 := ( 1, 9)( 2, 10)( 3, 14)( 4, 13)( 5, 12)( 6, 11)( 7, 16)( 8, 15)
( 17, 33)( 18, 34)( 19, 38)( 20, 37)( 21, 36)( 22, 35)( 23, 40)( 24, 39)
( 27, 30)( 28, 29)( 31, 32)( 41, 89)( 42, 90)( 43, 94)( 44, 93)( 45, 92)
( 46, 91)( 47, 96)( 48, 95)( 49, 81)( 50, 82)( 51, 86)( 52, 85)( 53, 84)
( 54, 83)( 55, 88)( 56, 87)( 57,113)( 58,114)( 59,118)( 60,117)( 61,116)
( 62,115)( 63,120)( 64,119)( 65,105)( 66,106)( 67,110)( 68,109)( 69,108)
( 70,107)( 71,112)( 72,111)( 73, 97)( 74, 98)( 75,102)( 76,101)( 77,100)
( 78, 99)( 79,104)( 80,103)(121,130)(122,129)(123,133)(124,134)(125,131)
(126,132)(127,135)(128,136)(137,154)(138,153)(139,157)(140,158)(141,155)
(142,156)(143,159)(144,160)(145,146)(147,149)(148,150)(161,210)(162,209)
(163,213)(164,214)(165,211)(166,212)(167,215)(168,216)(169,202)(170,201)
(171,205)(172,206)(173,203)(174,204)(175,207)(176,208)(177,234)(178,233)
(179,237)(180,238)(181,235)(182,236)(183,239)(184,240)(185,226)(186,225)
(187,229)(188,230)(189,227)(190,228)(191,231)(192,232)(193,218)(194,217)
(195,221)(196,222)(197,219)(198,220)(199,223)(200,224);;
s2 := ( 1,161)( 2,162)( 3,164)( 4,163)( 5,167)( 6,168)( 7,165)( 8,166)
( 9,169)( 10,170)( 11,172)( 12,171)( 13,175)( 14,176)( 15,173)( 16,174)
( 17,177)( 18,178)( 19,180)( 20,179)( 21,183)( 22,184)( 23,181)( 24,182)
( 25,185)( 26,186)( 27,188)( 28,187)( 29,191)( 30,192)( 31,189)( 32,190)
( 33,193)( 34,194)( 35,196)( 36,195)( 37,199)( 38,200)( 39,197)( 40,198)
( 41,121)( 42,122)( 43,124)( 44,123)( 45,127)( 46,128)( 47,125)( 48,126)
( 49,129)( 50,130)( 51,132)( 52,131)( 53,135)( 54,136)( 55,133)( 56,134)
( 57,137)( 58,138)( 59,140)( 60,139)( 61,143)( 62,144)( 63,141)( 64,142)
( 65,145)( 66,146)( 67,148)( 68,147)( 69,151)( 70,152)( 71,149)( 72,150)
( 73,153)( 74,154)( 75,156)( 76,155)( 77,159)( 78,160)( 79,157)( 80,158)
( 81,201)( 82,202)( 83,204)( 84,203)( 85,207)( 86,208)( 87,205)( 88,206)
( 89,209)( 90,210)( 91,212)( 92,211)( 93,215)( 94,216)( 95,213)( 96,214)
( 97,217)( 98,218)( 99,220)(100,219)(101,223)(102,224)(103,221)(104,222)
(105,225)(106,226)(107,228)(108,227)(109,231)(110,232)(111,229)(112,230)
(113,233)(114,234)(115,236)(116,235)(117,239)(118,240)(119,237)(120,238);;
s3 := ( 1,128)( 2,127)( 3,124)( 4,123)( 5,125)( 6,126)( 7,122)( 8,121)
( 9,136)( 10,135)( 11,132)( 12,131)( 13,133)( 14,134)( 15,130)( 16,129)
( 17,144)( 18,143)( 19,140)( 20,139)( 21,141)( 22,142)( 23,138)( 24,137)
( 25,152)( 26,151)( 27,148)( 28,147)( 29,149)( 30,150)( 31,146)( 32,145)
( 33,160)( 34,159)( 35,156)( 36,155)( 37,157)( 38,158)( 39,154)( 40,153)
( 41,208)( 42,207)( 43,204)( 44,203)( 45,205)( 46,206)( 47,202)( 48,201)
( 49,216)( 50,215)( 51,212)( 52,211)( 53,213)( 54,214)( 55,210)( 56,209)
( 57,224)( 58,223)( 59,220)( 60,219)( 61,221)( 62,222)( 63,218)( 64,217)
( 65,232)( 66,231)( 67,228)( 68,227)( 69,229)( 70,230)( 71,226)( 72,225)
( 73,240)( 74,239)( 75,236)( 76,235)( 77,237)( 78,238)( 79,234)( 80,233)
( 81,168)( 82,167)( 83,164)( 84,163)( 85,165)( 86,166)( 87,162)( 88,161)
( 89,176)( 90,175)( 91,172)( 92,171)( 93,173)( 94,174)( 95,170)( 96,169)
( 97,184)( 98,183)( 99,180)(100,179)(101,181)(102,182)(103,178)(104,177)
(105,192)(106,191)(107,188)(108,187)(109,189)(110,190)(111,186)(112,185)
(113,200)(114,199)(115,196)(116,195)(117,197)(118,198)(119,194)(120,193);;
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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s3*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(240)!( 9, 33)( 10, 34)( 11, 35)( 12, 36)( 13, 37)( 14, 38)( 15, 39)
( 16, 40)( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)
( 24, 32)( 49, 73)( 50, 74)( 51, 75)( 52, 76)( 53, 77)( 54, 78)( 55, 79)
( 56, 80)( 57, 65)( 58, 66)( 59, 67)( 60, 68)( 61, 69)( 62, 70)( 63, 71)
( 64, 72)( 89,113)( 90,114)( 91,115)( 92,116)( 93,117)( 94,118)( 95,119)
( 96,120)( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)
(104,112)(129,153)(130,154)(131,155)(132,156)(133,157)(134,158)(135,159)
(136,160)(137,145)(138,146)(139,147)(140,148)(141,149)(142,150)(143,151)
(144,152)(169,193)(170,194)(171,195)(172,196)(173,197)(174,198)(175,199)
(176,200)(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)
(184,192)(209,233)(210,234)(211,235)(212,236)(213,237)(214,238)(215,239)
(216,240)(217,225)(218,226)(219,227)(220,228)(221,229)(222,230)(223,231)
(224,232);
s1 := Sym(240)!( 1, 9)( 2, 10)( 3, 14)( 4, 13)( 5, 12)( 6, 11)( 7, 16)
( 8, 15)( 17, 33)( 18, 34)( 19, 38)( 20, 37)( 21, 36)( 22, 35)( 23, 40)
( 24, 39)( 27, 30)( 28, 29)( 31, 32)( 41, 89)( 42, 90)( 43, 94)( 44, 93)
( 45, 92)( 46, 91)( 47, 96)( 48, 95)( 49, 81)( 50, 82)( 51, 86)( 52, 85)
( 53, 84)( 54, 83)( 55, 88)( 56, 87)( 57,113)( 58,114)( 59,118)( 60,117)
( 61,116)( 62,115)( 63,120)( 64,119)( 65,105)( 66,106)( 67,110)( 68,109)
( 69,108)( 70,107)( 71,112)( 72,111)( 73, 97)( 74, 98)( 75,102)( 76,101)
( 77,100)( 78, 99)( 79,104)( 80,103)(121,130)(122,129)(123,133)(124,134)
(125,131)(126,132)(127,135)(128,136)(137,154)(138,153)(139,157)(140,158)
(141,155)(142,156)(143,159)(144,160)(145,146)(147,149)(148,150)(161,210)
(162,209)(163,213)(164,214)(165,211)(166,212)(167,215)(168,216)(169,202)
(170,201)(171,205)(172,206)(173,203)(174,204)(175,207)(176,208)(177,234)
(178,233)(179,237)(180,238)(181,235)(182,236)(183,239)(184,240)(185,226)
(186,225)(187,229)(188,230)(189,227)(190,228)(191,231)(192,232)(193,218)
(194,217)(195,221)(196,222)(197,219)(198,220)(199,223)(200,224);
s2 := Sym(240)!( 1,161)( 2,162)( 3,164)( 4,163)( 5,167)( 6,168)( 7,165)
( 8,166)( 9,169)( 10,170)( 11,172)( 12,171)( 13,175)( 14,176)( 15,173)
( 16,174)( 17,177)( 18,178)( 19,180)( 20,179)( 21,183)( 22,184)( 23,181)
( 24,182)( 25,185)( 26,186)( 27,188)( 28,187)( 29,191)( 30,192)( 31,189)
( 32,190)( 33,193)( 34,194)( 35,196)( 36,195)( 37,199)( 38,200)( 39,197)
( 40,198)( 41,121)( 42,122)( 43,124)( 44,123)( 45,127)( 46,128)( 47,125)
( 48,126)( 49,129)( 50,130)( 51,132)( 52,131)( 53,135)( 54,136)( 55,133)
( 56,134)( 57,137)( 58,138)( 59,140)( 60,139)( 61,143)( 62,144)( 63,141)
( 64,142)( 65,145)( 66,146)( 67,148)( 68,147)( 69,151)( 70,152)( 71,149)
( 72,150)( 73,153)( 74,154)( 75,156)( 76,155)( 77,159)( 78,160)( 79,157)
( 80,158)( 81,201)( 82,202)( 83,204)( 84,203)( 85,207)( 86,208)( 87,205)
( 88,206)( 89,209)( 90,210)( 91,212)( 92,211)( 93,215)( 94,216)( 95,213)
( 96,214)( 97,217)( 98,218)( 99,220)(100,219)(101,223)(102,224)(103,221)
(104,222)(105,225)(106,226)(107,228)(108,227)(109,231)(110,232)(111,229)
(112,230)(113,233)(114,234)(115,236)(116,235)(117,239)(118,240)(119,237)
(120,238);
s3 := Sym(240)!( 1,128)( 2,127)( 3,124)( 4,123)( 5,125)( 6,126)( 7,122)
( 8,121)( 9,136)( 10,135)( 11,132)( 12,131)( 13,133)( 14,134)( 15,130)
( 16,129)( 17,144)( 18,143)( 19,140)( 20,139)( 21,141)( 22,142)( 23,138)
( 24,137)( 25,152)( 26,151)( 27,148)( 28,147)( 29,149)( 30,150)( 31,146)
( 32,145)( 33,160)( 34,159)( 35,156)( 36,155)( 37,157)( 38,158)( 39,154)
( 40,153)( 41,208)( 42,207)( 43,204)( 44,203)( 45,205)( 46,206)( 47,202)
( 48,201)( 49,216)( 50,215)( 51,212)( 52,211)( 53,213)( 54,214)( 55,210)
( 56,209)( 57,224)( 58,223)( 59,220)( 60,219)( 61,221)( 62,222)( 63,218)
( 64,217)( 65,232)( 66,231)( 67,228)( 68,227)( 69,229)( 70,230)( 71,226)
( 72,225)( 73,240)( 74,239)( 75,236)( 76,235)( 77,237)( 78,238)( 79,234)
( 80,233)( 81,168)( 82,167)( 83,164)( 84,163)( 85,165)( 86,166)( 87,162)
( 88,161)( 89,176)( 90,175)( 91,172)( 92,171)( 93,173)( 94,174)( 95,170)
( 96,169)( 97,184)( 98,183)( 99,180)(100,179)(101,181)(102,182)(103,178)
(104,177)(105,192)(106,191)(107,188)(108,187)(109,189)(110,190)(111,186)
(112,185)(113,200)(114,199)(115,196)(116,195)(117,197)(118,198)(119,194)
(120,193);
poly := sub<Sym(240)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1,
s3*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope