Polytope of Type {10,14,7}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,14,7}*1960
if this polytope has a name.
Group : SmallGroup(1960,126)
Rank : 4
Schlafli Type : {10,14,7}
Number of vertices, edges, etc : 10, 70, 49, 7
Order of s0s1s2s3 : 70
Order of s0s1s2s3s2s1 : 2
Special Properties :
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) :
5-fold quotients : {2,14,7}*392
7-fold quotients : {10,2,7}*280
14-fold quotients : {5,2,7}*140
35-fold quotients : {2,2,7}*56
Covers (Minimal Covers in Boldface) :
None in this atlas.
Irregular Quotients (of which this is a minimal cover):
None.
Permutation Representation (GAP) :
s0 := ( 50,197)( 51,198)( 52,199)( 53,200)( 54,201)( 55,202)( 56,203)( 57,204)( 58,205)( 59,206)( 60,207)( 61,208)( 62,209)( 63,210)( 64,211)( 65,212)( 66,213)( 67,214)( 68,215)( 69,216)( 70,217)( 71,218)( 72,219)( 73,220)( 74,221)( 75,222)( 76,223)( 77,224)( 78,225)( 79,226)( 80,227)( 81,228)( 82,229)( 83,230)( 84,231)( 85,232)( 86,233)( 87,234)( 88,235)( 89,236)( 90,237)( 91,238)( 92,239)( 93,240)( 94,241)( 95,242)( 96,243)( 97,244)( 98,245)( 99,148)(100,149)(101,150)(102,151)(103,152)(104,153)(105,154)(106,155)(107,156)(108,157)(109,158)(110,159)(111,160)(112,161)(113,162)(114,163)(115,164)(116,165)(117,166)(118,167)(119,168)(120,169)(121,170)(122,171)(123,172)(124,173)(125,174)(126,175)(127,176)(128,177)(129,178)(130,179)(131,180)(132,181)(133,182)(134,183)(135,184)(136,185)(137,186)(138,187)(139,188)(140,189)(141,190)(142,191)(143,192)(144,193)(145,194)(146,195)(147,196);;
s1 := ( 1, 50)( 2, 51)( 3, 52)( 4, 53)( 5, 54)( 6, 55)( 7, 56)( 8, 92)( 9, 93)( 10, 94)( 11, 95)( 12, 96)( 13, 97)( 14, 98)( 15, 85)( 16, 86)( 17, 87)( 18, 88)( 19, 89)( 20, 90)( 21, 91)( 22, 78)( 23, 79)( 24, 80)( 25, 81)( 26, 82)( 27, 83)( 28, 84)( 29, 71)( 30, 72)( 31, 73)( 32, 74)( 33, 75)( 34, 76)( 35, 77)( 36, 64)( 37, 65)( 38, 66)( 39, 67)( 40, 68)( 41, 69)( 42, 70)( 43, 57)( 44, 58)( 45, 59)( 46, 60)( 47, 61)( 48, 62)( 49, 63)( 99,197)(100,198)(101,199)(102,200)(103,201)(104,202)(105,203)(106,239)(107,240)(108,241)(109,242)(110,243)(111,244)(112,245)(113,232)(114,233)(115,234)(116,235)(117,236)(118,237)(119,238)(120,225)(121,226)(122,227)(123,228)(124,229)(125,230)(126,231)(127,218)(128,219)(129,220)(130,221)(131,222)(132,223)(133,224)(134,211)(135,212)(136,213)(137,214)(138,215)(139,216)(140,217)(141,204)(142,205)(143,206)(144,207)(145,208)(146,209)(147,210)(155,190)(156,191)(157,192)(158,193)(159,194)(160,195)(161,196)(162,183)(163,184)(164,185)(165,186)(166,187)(167,188)(168,189)(169,176)(170,177)(171,178)(172,179)(173,180)(174,181)(175,182);;
s2 := ( 1, 8)( 2, 14)( 3, 13)( 4, 12)( 5, 11)( 6, 10)( 7, 9)( 15, 43)( 16, 49)( 17, 48)( 18, 47)( 19, 46)( 20, 45)( 21, 44)( 22, 36)( 23, 42)( 24, 41)( 25, 40)( 26, 39)( 27, 38)( 28, 37)( 30, 35)( 31, 34)( 32, 33)( 50, 57)( 51, 63)( 52, 62)( 53, 61)( 54, 60)( 55, 59)( 56, 58)( 64, 92)( 65, 98)( 66, 97)( 67, 96)( 68, 95)( 69, 94)( 70, 93)( 71, 85)( 72, 91)( 73, 90)( 74, 89)( 75, 88)( 76, 87)( 77, 86)( 79, 84)( 80, 83)( 81, 82)( 99,106)(100,112)(101,111)(102,110)(103,109)(104,108)(105,107)(113,141)(114,147)(115,146)(116,145)(117,144)(118,143)(119,142)(120,134)(121,140)(122,139)(123,138)(124,137)(125,136)(126,135)(128,133)(129,132)(130,131)(148,155)(149,161)(150,160)(151,159)(152,158)(153,157)(154,156)(162,190)(163,196)(164,195)(165,194)(166,193)(167,192)(168,191)(169,183)(170,189)(171,188)(172,187)(173,186)(174,185)(175,184)(177,182)(178,181)(179,180)(197,204)(198,210)(199,209)(200,208)(201,207)(202,206)(203,205)(211,239)(212,245)(213,244)(214,243)(215,242)(216,241)(217,240)(218,232)(219,238)(220,237)(221,236)(222,235)(223,234)(224,233)(226,231)(227,230)(228,229);;
s3 := ( 1, 2)( 3, 7)( 4, 6)( 8, 44)( 9, 43)( 10, 49)( 11, 48)( 12, 47)( 13, 46)( 14, 45)( 15, 37)( 16, 36)( 17, 42)( 18, 41)( 19, 40)( 20, 39)( 21, 38)( 22, 30)( 23, 29)( 24, 35)( 25, 34)( 26, 33)( 27, 32)( 28, 31)( 50, 51)( 52, 56)( 53, 55)( 57, 93)( 58, 92)( 59, 98)( 60, 97)( 61, 96)( 62, 95)( 63, 94)( 64, 86)( 65, 85)( 66, 91)( 67, 90)( 68, 89)( 69, 88)( 70, 87)( 71, 79)( 72, 78)( 73, 84)( 74, 83)( 75, 82)( 76, 81)( 77, 80)( 99,100)(101,105)(102,104)(106,142)(107,141)(108,147)(109,146)(110,145)(111,144)(112,143)(113,135)(114,134)(115,140)(116,139)(117,138)(118,137)(119,136)(120,128)(121,127)(122,133)(123,132)(124,131)(125,130)(126,129)(148,149)(150,154)(151,153)(155,191)(156,190)(157,196)(158,195)(159,194)(160,193)(161,192)(162,184)(163,183)(164,189)(165,188)(166,187)(167,186)(168,185)(169,177)(170,176)(171,182)(172,181)(173,180)(174,179)(175,178)(197,198)(199,203)(200,202)(204,240)(205,239)(206,245)(207,244)(208,243)(209,242)(210,241)(211,233)(212,232)(213,238)(214,237)(215,236)(216,235)(217,234)(218,226)(219,225)(220,231)(221,230)(222,229)(223,228)(224,227);;
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, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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(245)!( 50,197)( 51,198)( 52,199)( 53,200)( 54,201)( 55,202)( 56,203)( 57,204)( 58,205)( 59,206)( 60,207)( 61,208)( 62,209)( 63,210)( 64,211)( 65,212)( 66,213)( 67,214)( 68,215)( 69,216)( 70,217)( 71,218)( 72,219)( 73,220)( 74,221)( 75,222)( 76,223)( 77,224)( 78,225)( 79,226)( 80,227)( 81,228)( 82,229)( 83,230)( 84,231)( 85,232)( 86,233)( 87,234)( 88,235)( 89,236)( 90,237)( 91,238)( 92,239)( 93,240)( 94,241)( 95,242)( 96,243)( 97,244)( 98,245)( 99,148)(100,149)(101,150)(102,151)(103,152)(104,153)(105,154)(106,155)(107,156)(108,157)(109,158)(110,159)(111,160)(112,161)(113,162)(114,163)(115,164)(116,165)(117,166)(118,167)(119,168)(120,169)(121,170)(122,171)(123,172)(124,173)(125,174)(126,175)(127,176)(128,177)(129,178)(130,179)(131,180)(132,181)(133,182)(134,183)(135,184)(136,185)(137,186)(138,187)(139,188)(140,189)(141,190)(142,191)(143,192)(144,193)(145,194)(146,195)(147,196);
s1 := Sym(245)!( 1, 50)( 2, 51)( 3, 52)( 4, 53)( 5, 54)( 6, 55)( 7, 56)( 8, 92)( 9, 93)( 10, 94)( 11, 95)( 12, 96)( 13, 97)( 14, 98)( 15, 85)( 16, 86)( 17, 87)( 18, 88)( 19, 89)( 20, 90)( 21, 91)( 22, 78)( 23, 79)( 24, 80)( 25, 81)( 26, 82)( 27, 83)( 28, 84)( 29, 71)( 30, 72)( 31, 73)( 32, 74)( 33, 75)( 34, 76)( 35, 77)( 36, 64)( 37, 65)( 38, 66)( 39, 67)( 40, 68)( 41, 69)( 42, 70)( 43, 57)( 44, 58)( 45, 59)( 46, 60)( 47, 61)( 48, 62)( 49, 63)( 99,197)(100,198)(101,199)(102,200)(103,201)(104,202)(105,203)(106,239)(107,240)(108,241)(109,242)(110,243)(111,244)(112,245)(113,232)(114,233)(115,234)(116,235)(117,236)(118,237)(119,238)(120,225)(121,226)(122,227)(123,228)(124,229)(125,230)(126,231)(127,218)(128,219)(129,220)(130,221)(131,222)(132,223)(133,224)(134,211)(135,212)(136,213)(137,214)(138,215)(139,216)(140,217)(141,204)(142,205)(143,206)(144,207)(145,208)(146,209)(147,210)(155,190)(156,191)(157,192)(158,193)(159,194)(160,195)(161,196)(162,183)(163,184)(164,185)(165,186)(166,187)(167,188)(168,189)(169,176)(170,177)(171,178)(172,179)(173,180)(174,181)(175,182);
s2 := Sym(245)!( 1, 8)( 2, 14)( 3, 13)( 4, 12)( 5, 11)( 6, 10)( 7, 9)( 15, 43)( 16, 49)( 17, 48)( 18, 47)( 19, 46)( 20, 45)( 21, 44)( 22, 36)( 23, 42)( 24, 41)( 25, 40)( 26, 39)( 27, 38)( 28, 37)( 30, 35)( 31, 34)( 32, 33)( 50, 57)( 51, 63)( 52, 62)( 53, 61)( 54, 60)( 55, 59)( 56, 58)( 64, 92)( 65, 98)( 66, 97)( 67, 96)( 68, 95)( 69, 94)( 70, 93)( 71, 85)( 72, 91)( 73, 90)( 74, 89)( 75, 88)( 76, 87)( 77, 86)( 79, 84)( 80, 83)( 81, 82)( 99,106)(100,112)(101,111)(102,110)(103,109)(104,108)(105,107)(113,141)(114,147)(115,146)(116,145)(117,144)(118,143)(119,142)(120,134)(121,140)(122,139)(123,138)(124,137)(125,136)(126,135)(128,133)(129,132)(130,131)(148,155)(149,161)(150,160)(151,159)(152,158)(153,157)(154,156)(162,190)(163,196)(164,195)(165,194)(166,193)(167,192)(168,191)(169,183)(170,189)(171,188)(172,187)(173,186)(174,185)(175,184)(177,182)(178,181)(179,180)(197,204)(198,210)(199,209)(200,208)(201,207)(202,206)(203,205)(211,239)(212,245)(213,244)(214,243)(215,242)(216,241)(217,240)(218,232)(219,238)(220,237)(221,236)(222,235)(223,234)(224,233)(226,231)(227,230)(228,229);
s3 := Sym(245)!( 1, 2)( 3, 7)( 4, 6)( 8, 44)( 9, 43)( 10, 49)( 11, 48)( 12, 47)( 13, 46)( 14, 45)( 15, 37)( 16, 36)( 17, 42)( 18, 41)( 19, 40)( 20, 39)( 21, 38)( 22, 30)( 23, 29)( 24, 35)( 25, 34)( 26, 33)( 27, 32)( 28, 31)( 50, 51)( 52, 56)( 53, 55)( 57, 93)( 58, 92)( 59, 98)( 60, 97)( 61, 96)( 62, 95)( 63, 94)( 64, 86)( 65, 85)( 66, 91)( 67, 90)( 68, 89)( 69, 88)( 70, 87)( 71, 79)( 72, 78)( 73, 84)( 74, 83)( 75, 82)( 76, 81)( 77, 80)( 99,100)(101,105)(102,104)(106,142)(107,141)(108,147)(109,146)(110,145)(111,144)(112,143)(113,135)(114,134)(115,140)(116,139)(117,138)(118,137)(119,136)(120,128)(121,127)(122,133)(123,132)(124,131)(125,130)(126,129)(148,149)(150,154)(151,153)(155,191)(156,190)(157,196)(158,195)(159,194)(160,193)(161,192)(162,184)(163,183)(164,189)(165,188)(166,187)(167,186)(168,185)(169,177)(170,176)(171,182)(172,181)(173,180)(174,179)(175,178)(197,198)(199,203)(200,202)(204,240)(205,239)(206,245)(207,244)(208,243)(209,242)(210,241)(211,233)(212,232)(213,238)(214,237)(215,236)(216,235)(217,234)(218,226)(219,225)(220,231)(221,230)(222,229)(223,228)(224,227);
poly := sub<Sym(245)|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,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s1*s2*s1*s2*s3*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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