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.
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, 
s3*s1*s2*s1*s2*s3*s1*s2*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, s3*s1*s2*s1*s2*s3*s1*s2*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