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