Polytope of Type {14,20}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,20}*1960
if this polytope has a name.
Group : SmallGroup(1960,123)
Rank : 3
Schlafli Type : {14,20}
Number of vertices, edges, etc : 49, 490, 70
Order of s0s1s2 : 20
Order of s0s1s2s1 : 14
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
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 : {14,4}*392
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, 8)( 2, 9)( 3, 10)( 4, 11)( 5, 12)( 6, 13)( 7, 14)( 15, 43)
( 16, 44)( 17, 45)( 18, 46)( 19, 47)( 20, 48)( 21, 49)( 22, 36)( 23, 37)
( 24, 38)( 25, 39)( 26, 40)( 27, 41)( 28, 42)( 50,204)( 51,205)( 52,206)
( 53,207)( 54,208)( 55,209)( 56,210)( 57,197)( 58,198)( 59,199)( 60,200)
( 61,201)( 62,202)( 63,203)( 64,239)( 65,240)( 66,241)( 67,242)( 68,243)
( 69,244)( 70,245)( 71,232)( 72,233)( 73,234)( 74,235)( 75,236)( 76,237)
( 77,238)( 78,225)( 79,226)( 80,227)( 81,228)( 82,229)( 83,230)( 84,231)
( 85,218)( 86,219)( 87,220)( 88,221)( 89,222)( 90,223)( 91,224)( 92,211)
( 93,212)( 94,213)( 95,214)( 96,215)( 97,216)( 98,217)( 99,155)(100,156)
(101,157)(102,158)(103,159)(104,160)(105,161)(106,148)(107,149)(108,150)
(109,151)(110,152)(111,153)(112,154)(113,190)(114,191)(115,192)(116,193)
(117,194)(118,195)(119,196)(120,183)(121,184)(122,185)(123,186)(124,187)
(125,188)(126,189)(127,176)(128,177)(129,178)(130,179)(131,180)(132,181)
(133,182)(134,169)(135,170)(136,171)(137,172)(138,173)(139,174)(140,175)
(141,162)(142,163)(143,164)(144,165)(145,166)(146,167)(147,168);;
s2 := ( 1, 50)( 2, 57)( 3, 64)( 4, 71)( 5, 78)( 6, 85)( 7, 92)( 8, 51)
( 9, 58)( 10, 65)( 11, 72)( 12, 79)( 13, 86)( 14, 93)( 15, 52)( 16, 59)
( 17, 66)( 18, 73)( 19, 80)( 20, 87)( 21, 94)( 22, 53)( 23, 60)( 24, 67)
( 25, 74)( 26, 81)( 27, 88)( 28, 95)( 29, 54)( 30, 61)( 31, 68)( 32, 75)
( 33, 82)( 34, 89)( 35, 96)( 36, 55)( 37, 62)( 38, 69)( 39, 76)( 40, 83)
( 41, 90)( 42, 97)( 43, 56)( 44, 63)( 45, 70)( 46, 77)( 47, 84)( 48, 91)
( 49, 98)( 99,197)(100,204)(101,211)(102,218)(103,225)(104,232)(105,239)
(106,198)(107,205)(108,212)(109,219)(110,226)(111,233)(112,240)(113,199)
(114,206)(115,213)(116,220)(117,227)(118,234)(119,241)(120,200)(121,207)
(122,214)(123,221)(124,228)(125,235)(126,242)(127,201)(128,208)(129,215)
(130,222)(131,229)(132,236)(133,243)(134,202)(135,209)(136,216)(137,223)
(138,230)(139,237)(140,244)(141,203)(142,210)(143,217)(144,224)(145,231)
(146,238)(147,245)(149,155)(150,162)(151,169)(152,176)(153,183)(154,190)
(157,163)(158,170)(159,177)(160,184)(161,191)(165,171)(166,178)(167,185)
(168,192)(173,179)(174,186)(175,193)(181,187)(182,194)(189,195);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2 ];;
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, 8)( 2, 9)( 3, 10)( 4, 11)( 5, 12)( 6, 13)( 7, 14)
( 15, 43)( 16, 44)( 17, 45)( 18, 46)( 19, 47)( 20, 48)( 21, 49)( 22, 36)
( 23, 37)( 24, 38)( 25, 39)( 26, 40)( 27, 41)( 28, 42)( 50,204)( 51,205)
( 52,206)( 53,207)( 54,208)( 55,209)( 56,210)( 57,197)( 58,198)( 59,199)
( 60,200)( 61,201)( 62,202)( 63,203)( 64,239)( 65,240)( 66,241)( 67,242)
( 68,243)( 69,244)( 70,245)( 71,232)( 72,233)( 73,234)( 74,235)( 75,236)
( 76,237)( 77,238)( 78,225)( 79,226)( 80,227)( 81,228)( 82,229)( 83,230)
( 84,231)( 85,218)( 86,219)( 87,220)( 88,221)( 89,222)( 90,223)( 91,224)
( 92,211)( 93,212)( 94,213)( 95,214)( 96,215)( 97,216)( 98,217)( 99,155)
(100,156)(101,157)(102,158)(103,159)(104,160)(105,161)(106,148)(107,149)
(108,150)(109,151)(110,152)(111,153)(112,154)(113,190)(114,191)(115,192)
(116,193)(117,194)(118,195)(119,196)(120,183)(121,184)(122,185)(123,186)
(124,187)(125,188)(126,189)(127,176)(128,177)(129,178)(130,179)(131,180)
(132,181)(133,182)(134,169)(135,170)(136,171)(137,172)(138,173)(139,174)
(140,175)(141,162)(142,163)(143,164)(144,165)(145,166)(146,167)(147,168);
s2 := Sym(245)!( 1, 50)( 2, 57)( 3, 64)( 4, 71)( 5, 78)( 6, 85)( 7, 92)
( 8, 51)( 9, 58)( 10, 65)( 11, 72)( 12, 79)( 13, 86)( 14, 93)( 15, 52)
( 16, 59)( 17, 66)( 18, 73)( 19, 80)( 20, 87)( 21, 94)( 22, 53)( 23, 60)
( 24, 67)( 25, 74)( 26, 81)( 27, 88)( 28, 95)( 29, 54)( 30, 61)( 31, 68)
( 32, 75)( 33, 82)( 34, 89)( 35, 96)( 36, 55)( 37, 62)( 38, 69)( 39, 76)
( 40, 83)( 41, 90)( 42, 97)( 43, 56)( 44, 63)( 45, 70)( 46, 77)( 47, 84)
( 48, 91)( 49, 98)( 99,197)(100,204)(101,211)(102,218)(103,225)(104,232)
(105,239)(106,198)(107,205)(108,212)(109,219)(110,226)(111,233)(112,240)
(113,199)(114,206)(115,213)(116,220)(117,227)(118,234)(119,241)(120,200)
(121,207)(122,214)(123,221)(124,228)(125,235)(126,242)(127,201)(128,208)
(129,215)(130,222)(131,229)(132,236)(133,243)(134,202)(135,209)(136,216)
(137,223)(138,230)(139,237)(140,244)(141,203)(142,210)(143,217)(144,224)
(145,231)(146,238)(147,245)(149,155)(150,162)(151,169)(152,176)(153,183)
(154,190)(157,163)(158,170)(159,177)(160,184)(161,191)(165,171)(166,178)
(167,185)(168,192)(173,179)(174,186)(175,193)(181,187)(182,194)(189,195);
poly := sub<Sym(245)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2 >;
References : None.
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