Polytope of Type {14,4,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,4,4}*1568
if this polytope has a name.
Group : SmallGroup(1568,821)
Rank : 4
Schlafli Type : {14,4,4}
Number of vertices, edges, etc : 49, 98, 28, 4
Order of s0s1s2s3 : 4
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Non-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) :
2-fold quotients : {14,4,2}*784
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);;
s1 := ( 1, 8)( 3, 45)( 4, 39)( 5, 33)( 6, 27)( 7, 21)( 9, 44)( 10, 38)
( 11, 32)( 12, 26)( 13, 20)( 15, 43)( 16, 37)( 17, 31)( 18, 25)( 22, 36)
( 23, 30)( 28, 49)( 34, 48)( 35, 42)( 40, 47)( 50, 57)( 52, 94)( 53, 88)
( 54, 82)( 55, 76)( 56, 70)( 58, 93)( 59, 87)( 60, 81)( 61, 75)( 62, 69)
( 64, 92)( 65, 86)( 66, 80)( 67, 74)( 71, 85)( 72, 79)( 77, 98)( 83, 97)
( 84, 91)( 89, 96)( 99,106)(101,143)(102,137)(103,131)(104,125)(105,119)
(107,142)(108,136)(109,130)(110,124)(111,118)(113,141)(114,135)(115,129)
(116,123)(120,134)(121,128)(126,147)(132,146)(133,140)(138,145)(148,155)
(150,192)(151,186)(152,180)(153,174)(154,168)(156,191)(157,185)(158,179)
(159,173)(160,167)(162,190)(163,184)(164,178)(165,172)(169,183)(170,177)
(175,196)(181,195)(182,189)(187,194);;
s2 := ( 8, 45)( 9, 46)( 10, 47)( 11, 48)( 12, 49)( 13, 43)( 14, 44)( 15, 40)
( 16, 41)( 17, 42)( 18, 36)( 19, 37)( 20, 38)( 21, 39)( 22, 35)( 23, 29)
( 24, 30)( 25, 31)( 26, 32)( 27, 33)( 28, 34)( 57, 94)( 58, 95)( 59, 96)
( 60, 97)( 61, 98)( 62, 92)( 63, 93)( 64, 89)( 65, 90)( 66, 91)( 67, 85)
( 68, 86)( 69, 87)( 70, 88)( 71, 84)( 72, 78)( 73, 79)( 74, 80)( 75, 81)
( 76, 82)( 77, 83)( 99,148)(100,149)(101,150)(102,151)(103,152)(104,153)
(105,154)(106,192)(107,193)(108,194)(109,195)(110,196)(111,190)(112,191)
(113,187)(114,188)(115,189)(116,183)(117,184)(118,185)(119,186)(120,182)
(121,176)(122,177)(123,178)(124,179)(125,180)(126,181)(127,170)(128,171)
(129,172)(130,173)(131,174)(132,175)(133,169)(134,165)(135,166)(136,167)
(137,168)(138,162)(139,163)(140,164)(141,160)(142,161)(143,155)(144,156)
(145,157)(146,158)(147,159);;
s3 := ( 1, 99)( 2,100)( 3,101)( 4,102)( 5,103)( 6,104)( 7,105)( 8,106)
( 9,107)( 10,108)( 11,109)( 12,110)( 13,111)( 14,112)( 15,113)( 16,114)
( 17,115)( 18,116)( 19,117)( 20,118)( 21,119)( 22,120)( 23,121)( 24,122)
( 25,123)( 26,124)( 27,125)( 28,126)( 29,127)( 30,128)( 31,129)( 32,130)
( 33,131)( 34,132)( 35,133)( 36,134)( 37,135)( 38,136)( 39,137)( 40,138)
( 41,139)( 42,140)( 43,141)( 44,142)( 45,143)( 46,144)( 47,145)( 48,146)
( 49,147)( 50,148)( 51,149)( 52,150)( 53,151)( 54,152)( 55,153)( 56,154)
( 57,155)( 58,156)( 59,157)( 60,158)( 61,159)( 62,160)( 63,161)( 64,162)
( 65,163)( 66,164)( 67,165)( 68,166)( 69,167)( 70,168)( 71,169)( 72,170)
( 73,171)( 74,172)( 75,173)( 76,174)( 77,175)( 78,176)( 79,177)( 80,178)
( 81,179)( 82,180)( 83,181)( 84,182)( 85,183)( 86,184)( 87,185)( 88,186)
( 89,187)( 90,188)( 91,189)( 92,190)( 93,191)( 94,192)( 95,193)( 96,194)
( 97,195)( 98,196);;
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*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*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*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(196)!( 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);
s1 := Sym(196)!( 1, 8)( 3, 45)( 4, 39)( 5, 33)( 6, 27)( 7, 21)( 9, 44)
( 10, 38)( 11, 32)( 12, 26)( 13, 20)( 15, 43)( 16, 37)( 17, 31)( 18, 25)
( 22, 36)( 23, 30)( 28, 49)( 34, 48)( 35, 42)( 40, 47)( 50, 57)( 52, 94)
( 53, 88)( 54, 82)( 55, 76)( 56, 70)( 58, 93)( 59, 87)( 60, 81)( 61, 75)
( 62, 69)( 64, 92)( 65, 86)( 66, 80)( 67, 74)( 71, 85)( 72, 79)( 77, 98)
( 83, 97)( 84, 91)( 89, 96)( 99,106)(101,143)(102,137)(103,131)(104,125)
(105,119)(107,142)(108,136)(109,130)(110,124)(111,118)(113,141)(114,135)
(115,129)(116,123)(120,134)(121,128)(126,147)(132,146)(133,140)(138,145)
(148,155)(150,192)(151,186)(152,180)(153,174)(154,168)(156,191)(157,185)
(158,179)(159,173)(160,167)(162,190)(163,184)(164,178)(165,172)(169,183)
(170,177)(175,196)(181,195)(182,189)(187,194);
s2 := Sym(196)!( 8, 45)( 9, 46)( 10, 47)( 11, 48)( 12, 49)( 13, 43)( 14, 44)
( 15, 40)( 16, 41)( 17, 42)( 18, 36)( 19, 37)( 20, 38)( 21, 39)( 22, 35)
( 23, 29)( 24, 30)( 25, 31)( 26, 32)( 27, 33)( 28, 34)( 57, 94)( 58, 95)
( 59, 96)( 60, 97)( 61, 98)( 62, 92)( 63, 93)( 64, 89)( 65, 90)( 66, 91)
( 67, 85)( 68, 86)( 69, 87)( 70, 88)( 71, 84)( 72, 78)( 73, 79)( 74, 80)
( 75, 81)( 76, 82)( 77, 83)( 99,148)(100,149)(101,150)(102,151)(103,152)
(104,153)(105,154)(106,192)(107,193)(108,194)(109,195)(110,196)(111,190)
(112,191)(113,187)(114,188)(115,189)(116,183)(117,184)(118,185)(119,186)
(120,182)(121,176)(122,177)(123,178)(124,179)(125,180)(126,181)(127,170)
(128,171)(129,172)(130,173)(131,174)(132,175)(133,169)(134,165)(135,166)
(136,167)(137,168)(138,162)(139,163)(140,164)(141,160)(142,161)(143,155)
(144,156)(145,157)(146,158)(147,159);
s3 := Sym(196)!( 1, 99)( 2,100)( 3,101)( 4,102)( 5,103)( 6,104)( 7,105)
( 8,106)( 9,107)( 10,108)( 11,109)( 12,110)( 13,111)( 14,112)( 15,113)
( 16,114)( 17,115)( 18,116)( 19,117)( 20,118)( 21,119)( 22,120)( 23,121)
( 24,122)( 25,123)( 26,124)( 27,125)( 28,126)( 29,127)( 30,128)( 31,129)
( 32,130)( 33,131)( 34,132)( 35,133)( 36,134)( 37,135)( 38,136)( 39,137)
( 40,138)( 41,139)( 42,140)( 43,141)( 44,142)( 45,143)( 46,144)( 47,145)
( 48,146)( 49,147)( 50,148)( 51,149)( 52,150)( 53,151)( 54,152)( 55,153)
( 56,154)( 57,155)( 58,156)( 59,157)( 60,158)( 61,159)( 62,160)( 63,161)
( 64,162)( 65,163)( 66,164)( 67,165)( 68,166)( 69,167)( 70,168)( 71,169)
( 72,170)( 73,171)( 74,172)( 75,173)( 76,174)( 77,175)( 78,176)( 79,177)
( 80,178)( 81,179)( 82,180)( 83,181)( 84,182)( 85,183)( 86,184)( 87,185)
( 88,186)( 89,187)( 90,188)( 91,189)( 92,190)( 93,191)( 94,192)( 95,193)
( 96,194)( 97,195)( 98,196);
poly := sub<Sym(196)|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*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*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*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope