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