Polytope of Type {4,14,14}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,14,14}*1568b
if this polytope has a name.
Group : SmallGroup(1568,858)
Rank : 4
Schlafli Type : {4,14,14}
Number of vertices, edges, etc : 4, 28, 98, 14
Order of s0s1s2s3 : 28
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) :
2-fold quotients : {2,14,14}*784c
4-fold quotients : {2,7,14}*392
7-fold quotients : {4,14,2}*224
14-fold quotients : {2,14,2}*112
28-fold quotients : {2,7,2}*56
49-fold quotients : {4,2,2}*32
98-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Irregular Quotients (of which this is a minimal cover):
None.
Permutation Representation (GAP) :
s0 := ( 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, 99)( 2,105)( 3,104)( 4,103)( 5,102)( 6,101)( 7,100)( 8,141)( 9,147)( 10,146)( 11,145)( 12,144)( 13,143)( 14,142)( 15,134)( 16,140)( 17,139)( 18,138)( 19,137)( 20,136)( 21,135)( 22,127)( 23,133)( 24,132)( 25,131)( 26,130)( 27,129)( 28,128)( 29,120)( 30,126)( 31,125)( 32,124)( 33,123)( 34,122)( 35,121)( 36,113)( 37,119)( 38,118)( 39,117)( 40,116)( 41,115)( 42,114)( 43,106)( 44,112)( 45,111)( 46,110)( 47,109)( 48,108)( 49,107)( 50,148)( 51,154)( 52,153)( 53,152)( 54,151)( 55,150)( 56,149)( 57,190)( 58,196)( 59,195)( 60,194)( 61,193)( 62,192)( 63,191)( 64,183)( 65,189)( 66,188)( 67,187)( 68,186)( 69,185)( 70,184)( 71,176)( 72,182)( 73,181)( 74,180)( 75,179)( 76,178)( 77,177)( 78,169)( 79,175)( 80,174)( 81,173)( 82,172)( 83,171)( 84,170)( 85,162)( 86,168)( 87,167)( 88,166)( 89,165)( 90,164)( 91,163)( 92,155)( 93,161)( 94,160)( 95,159)( 96,158)( 97,157)( 98,156);;
s2 := ( 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);;
s3 := ( 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)( 57, 92)( 58, 93)( 59, 94)( 60, 95)( 61, 96)( 62, 97)( 63, 98)( 64, 85)( 65, 86)( 66, 87)( 67, 88)( 68, 89)( 69, 90)( 70, 91)( 71, 78)( 72, 79)( 73, 80)( 74, 81)( 75, 82)( 76, 83)( 77, 84)(106,141)(107,142)(108,143)(109,144)(110,145)(111,146)(112,147)(113,134)(114,135)(115,136)(116,137)(117,138)(118,139)(119,140)(120,127)(121,128)(122,129)(123,130)(124,131)(125,132)(126,133)(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);;
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, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(196)!( 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(196)!( 1, 99)( 2,105)( 3,104)( 4,103)( 5,102)( 6,101)( 7,100)( 8,141)( 9,147)( 10,146)( 11,145)( 12,144)( 13,143)( 14,142)( 15,134)( 16,140)( 17,139)( 18,138)( 19,137)( 20,136)( 21,135)( 22,127)( 23,133)( 24,132)( 25,131)( 26,130)( 27,129)( 28,128)( 29,120)( 30,126)( 31,125)( 32,124)( 33,123)( 34,122)( 35,121)( 36,113)( 37,119)( 38,118)( 39,117)( 40,116)( 41,115)( 42,114)( 43,106)( 44,112)( 45,111)( 46,110)( 47,109)( 48,108)( 49,107)( 50,148)( 51,154)( 52,153)( 53,152)( 54,151)( 55,150)( 56,149)( 57,190)( 58,196)( 59,195)( 60,194)( 61,193)( 62,192)( 63,191)( 64,183)( 65,189)( 66,188)( 67,187)( 68,186)( 69,185)( 70,184)( 71,176)( 72,182)( 73,181)( 74,180)( 75,179)( 76,178)( 77,177)( 78,169)( 79,175)( 80,174)( 81,173)( 82,172)( 83,171)( 84,170)( 85,162)( 86,168)( 87,167)( 88,166)( 89,165)( 90,164)( 91,163)( 92,155)( 93,161)( 94,160)( 95,159)( 96,158)( 97,157)( 98,156);
s2 := Sym(196)!( 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);
s3 := Sym(196)!( 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)( 57, 92)( 58, 93)( 59, 94)( 60, 95)( 61, 96)( 62, 97)( 63, 98)( 64, 85)( 65, 86)( 66, 87)( 67, 88)( 68, 89)( 69, 90)( 70, 91)( 71, 78)( 72, 79)( 73, 80)( 74, 81)( 75, 82)( 76, 83)( 77, 84)(106,141)(107,142)(108,143)(109,144)(110,145)(111,146)(112,147)(113,134)(114,135)(115,136)(116,137)(117,138)(118,139)(119,140)(120,127)(121,128)(122,129)(123,130)(124,131)(125,132)(126,133)(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);
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,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2 >;
References : None.
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