Polytope of Type {2,7,14,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,7,14,4}*1568
if this polytope has a name.
Group : SmallGroup(1568,877)
Rank : 5
Schlafli Type : {2,7,14,4}
Number of vertices, edges, etc : 2, 7, 49, 28, 4
Order of s0s1s2s3s4 : 28
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
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 : {2,7,14,2}*784
7-fold quotients : {2,7,2,4}*224
14-fold quotients : {2,7,2,2}*112
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 9)( 5, 8)( 6, 7)( 10, 45)( 11, 51)( 12, 50)( 13, 49)( 14, 48)
( 15, 47)( 16, 46)( 17, 38)( 18, 44)( 19, 43)( 20, 42)( 21, 41)( 22, 40)
( 23, 39)( 24, 31)( 25, 37)( 26, 36)( 27, 35)( 28, 34)( 29, 33)( 30, 32)
( 53, 58)( 54, 57)( 55, 56)( 59, 94)( 60,100)( 61, 99)( 62, 98)( 63, 97)
( 64, 96)( 65, 95)( 66, 87)( 67, 93)( 68, 92)( 69, 91)( 70, 90)( 71, 89)
( 72, 88)( 73, 80)( 74, 86)( 75, 85)( 76, 84)( 77, 83)( 78, 82)( 79, 81)
(102,107)(103,106)(104,105)(108,143)(109,149)(110,148)(111,147)(112,146)
(113,145)(114,144)(115,136)(116,142)(117,141)(118,140)(119,139)(120,138)
(121,137)(122,129)(123,135)(124,134)(125,133)(126,132)(127,131)(128,130)
(151,156)(152,155)(153,154)(157,192)(158,198)(159,197)(160,196)(161,195)
(162,194)(163,193)(164,185)(165,191)(166,190)(167,189)(168,188)(169,187)
(170,186)(171,178)(172,184)(173,183)(174,182)(175,181)(176,180)(177,179);;
s2 := ( 3, 11)( 4, 10)( 5, 16)( 6, 15)( 7, 14)( 8, 13)( 9, 12)( 17, 46)
( 18, 45)( 19, 51)( 20, 50)( 21, 49)( 22, 48)( 23, 47)( 24, 39)( 25, 38)
( 26, 44)( 27, 43)( 28, 42)( 29, 41)( 30, 40)( 31, 32)( 33, 37)( 34, 36)
( 52, 60)( 53, 59)( 54, 65)( 55, 64)( 56, 63)( 57, 62)( 58, 61)( 66, 95)
( 67, 94)( 68,100)( 69, 99)( 70, 98)( 71, 97)( 72, 96)( 73, 88)( 74, 87)
( 75, 93)( 76, 92)( 77, 91)( 78, 90)( 79, 89)( 80, 81)( 82, 86)( 83, 85)
(101,109)(102,108)(103,114)(104,113)(105,112)(106,111)(107,110)(115,144)
(116,143)(117,149)(118,148)(119,147)(120,146)(121,145)(122,137)(123,136)
(124,142)(125,141)(126,140)(127,139)(128,138)(129,130)(131,135)(132,134)
(150,158)(151,157)(152,163)(153,162)(154,161)(155,160)(156,159)(164,193)
(165,192)(166,198)(167,197)(168,196)(169,195)(170,194)(171,186)(172,185)
(173,191)(174,190)(175,189)(176,188)(177,187)(178,179)(180,184)(181,183);;
s3 := ( 4, 9)( 5, 8)( 6, 7)( 11, 16)( 12, 15)( 13, 14)( 18, 23)( 19, 22)
( 20, 21)( 25, 30)( 26, 29)( 27, 28)( 32, 37)( 33, 36)( 34, 35)( 39, 44)
( 40, 43)( 41, 42)( 46, 51)( 47, 50)( 48, 49)( 53, 58)( 54, 57)( 55, 56)
( 60, 65)( 61, 64)( 62, 63)( 67, 72)( 68, 71)( 69, 70)( 74, 79)( 75, 78)
( 76, 77)( 81, 86)( 82, 85)( 83, 84)( 88, 93)( 89, 92)( 90, 91)( 95,100)
( 96, 99)( 97, 98)(101,150)(102,156)(103,155)(104,154)(105,153)(106,152)
(107,151)(108,157)(109,163)(110,162)(111,161)(112,160)(113,159)(114,158)
(115,164)(116,170)(117,169)(118,168)(119,167)(120,166)(121,165)(122,171)
(123,177)(124,176)(125,175)(126,174)(127,173)(128,172)(129,178)(130,184)
(131,183)(132,182)(133,181)(134,180)(135,179)(136,185)(137,191)(138,190)
(139,189)(140,188)(141,187)(142,186)(143,192)(144,198)(145,197)(146,196)
(147,195)(148,194)(149,193);;
s4 := ( 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)
( 99,197)(100,198);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(198)!(1,2);
s1 := Sym(198)!( 4, 9)( 5, 8)( 6, 7)( 10, 45)( 11, 51)( 12, 50)( 13, 49)
( 14, 48)( 15, 47)( 16, 46)( 17, 38)( 18, 44)( 19, 43)( 20, 42)( 21, 41)
( 22, 40)( 23, 39)( 24, 31)( 25, 37)( 26, 36)( 27, 35)( 28, 34)( 29, 33)
( 30, 32)( 53, 58)( 54, 57)( 55, 56)( 59, 94)( 60,100)( 61, 99)( 62, 98)
( 63, 97)( 64, 96)( 65, 95)( 66, 87)( 67, 93)( 68, 92)( 69, 91)( 70, 90)
( 71, 89)( 72, 88)( 73, 80)( 74, 86)( 75, 85)( 76, 84)( 77, 83)( 78, 82)
( 79, 81)(102,107)(103,106)(104,105)(108,143)(109,149)(110,148)(111,147)
(112,146)(113,145)(114,144)(115,136)(116,142)(117,141)(118,140)(119,139)
(120,138)(121,137)(122,129)(123,135)(124,134)(125,133)(126,132)(127,131)
(128,130)(151,156)(152,155)(153,154)(157,192)(158,198)(159,197)(160,196)
(161,195)(162,194)(163,193)(164,185)(165,191)(166,190)(167,189)(168,188)
(169,187)(170,186)(171,178)(172,184)(173,183)(174,182)(175,181)(176,180)
(177,179);
s2 := Sym(198)!( 3, 11)( 4, 10)( 5, 16)( 6, 15)( 7, 14)( 8, 13)( 9, 12)
( 17, 46)( 18, 45)( 19, 51)( 20, 50)( 21, 49)( 22, 48)( 23, 47)( 24, 39)
( 25, 38)( 26, 44)( 27, 43)( 28, 42)( 29, 41)( 30, 40)( 31, 32)( 33, 37)
( 34, 36)( 52, 60)( 53, 59)( 54, 65)( 55, 64)( 56, 63)( 57, 62)( 58, 61)
( 66, 95)( 67, 94)( 68,100)( 69, 99)( 70, 98)( 71, 97)( 72, 96)( 73, 88)
( 74, 87)( 75, 93)( 76, 92)( 77, 91)( 78, 90)( 79, 89)( 80, 81)( 82, 86)
( 83, 85)(101,109)(102,108)(103,114)(104,113)(105,112)(106,111)(107,110)
(115,144)(116,143)(117,149)(118,148)(119,147)(120,146)(121,145)(122,137)
(123,136)(124,142)(125,141)(126,140)(127,139)(128,138)(129,130)(131,135)
(132,134)(150,158)(151,157)(152,163)(153,162)(154,161)(155,160)(156,159)
(164,193)(165,192)(166,198)(167,197)(168,196)(169,195)(170,194)(171,186)
(172,185)(173,191)(174,190)(175,189)(176,188)(177,187)(178,179)(180,184)
(181,183);
s3 := Sym(198)!( 4, 9)( 5, 8)( 6, 7)( 11, 16)( 12, 15)( 13, 14)( 18, 23)
( 19, 22)( 20, 21)( 25, 30)( 26, 29)( 27, 28)( 32, 37)( 33, 36)( 34, 35)
( 39, 44)( 40, 43)( 41, 42)( 46, 51)( 47, 50)( 48, 49)( 53, 58)( 54, 57)
( 55, 56)( 60, 65)( 61, 64)( 62, 63)( 67, 72)( 68, 71)( 69, 70)( 74, 79)
( 75, 78)( 76, 77)( 81, 86)( 82, 85)( 83, 84)( 88, 93)( 89, 92)( 90, 91)
( 95,100)( 96, 99)( 97, 98)(101,150)(102,156)(103,155)(104,154)(105,153)
(106,152)(107,151)(108,157)(109,163)(110,162)(111,161)(112,160)(113,159)
(114,158)(115,164)(116,170)(117,169)(118,168)(119,167)(120,166)(121,165)
(122,171)(123,177)(124,176)(125,175)(126,174)(127,173)(128,172)(129,178)
(130,184)(131,183)(132,182)(133,181)(134,180)(135,179)(136,185)(137,191)
(138,190)(139,189)(140,188)(141,187)(142,186)(143,192)(144,198)(145,197)
(146,196)(147,195)(148,194)(149,193);
s4 := Sym(198)!( 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)( 99,197)(100,198);
poly := sub<Sym(198)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope