Polytope of Type {196,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {196,2}*784
if this polytope has a name.
Group : SmallGroup(784,29)
Rank : 3
Schlafli Type : {196,2}
Number of vertices, edges, etc : 196, 196, 2
Order of s0s1s2 : 196
Order of s0s1s2s1 : 2
Special Properties :
Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{196,2,2} of size 1568
Vertex Figure Of :
{2,196,2} of size 1568
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {98,2}*392
4-fold quotients : {49,2}*196
7-fold quotients : {28,2}*112
14-fold quotients : {14,2}*56
28-fold quotients : {7,2}*28
49-fold quotients : {4,2}*16
98-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {196,4}*1568, {392,2}*1568
Permutation Representation (GAP) :
s0 := ( 2, 7)( 3, 6)( 4, 5)( 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)
( 51, 56)( 52, 55)( 53, 54)( 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)
( 99,148)(100,154)(101,153)(102,152)(103,151)(104,150)(105,149)(106,191)
(107,190)(108,196)(109,195)(110,194)(111,193)(112,192)(113,184)(114,183)
(115,189)(116,188)(117,187)(118,186)(119,185)(120,177)(121,176)(122,182)
(123,181)(124,180)(125,179)(126,178)(127,170)(128,169)(129,175)(130,174)
(131,173)(132,172)(133,171)(134,163)(135,162)(136,168)(137,167)(138,166)
(139,165)(140,164)(141,156)(142,155)(143,161)(144,160)(145,159)(146,158)
(147,157);;
s1 := ( 1,106)( 2,112)( 3,111)( 4,110)( 5,109)( 6,108)( 7,107)( 8, 99)
( 9,105)( 10,104)( 11,103)( 12,102)( 13,101)( 14,100)( 15,142)( 16,141)
( 17,147)( 18,146)( 19,145)( 20,144)( 21,143)( 22,135)( 23,134)( 24,140)
( 25,139)( 26,138)( 27,137)( 28,136)( 29,128)( 30,127)( 31,133)( 32,132)
( 33,131)( 34,130)( 35,129)( 36,121)( 37,120)( 38,126)( 39,125)( 40,124)
( 41,123)( 42,122)( 43,114)( 44,113)( 45,119)( 46,118)( 47,117)( 48,116)
( 49,115)( 50,155)( 51,161)( 52,160)( 53,159)( 54,158)( 55,157)( 56,156)
( 57,148)( 58,154)( 59,153)( 60,152)( 61,151)( 62,150)( 63,149)( 64,191)
( 65,190)( 66,196)( 67,195)( 68,194)( 69,193)( 70,192)( 71,184)( 72,183)
( 73,189)( 74,188)( 75,187)( 76,186)( 77,185)( 78,177)( 79,176)( 80,182)
( 81,181)( 82,180)( 83,179)( 84,178)( 85,170)( 86,169)( 87,175)( 88,174)
( 89,173)( 90,172)( 91,171)( 92,163)( 93,162)( 94,168)( 95,167)( 96,166)
( 97,165)( 98,164);;
s2 := (197,198);;
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, s1*s2*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*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*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*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*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*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*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*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*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*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*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(198)!( 2, 7)( 3, 6)( 4, 5)( 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)( 51, 56)( 52, 55)( 53, 54)( 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)( 99,148)(100,154)(101,153)(102,152)(103,151)(104,150)(105,149)
(106,191)(107,190)(108,196)(109,195)(110,194)(111,193)(112,192)(113,184)
(114,183)(115,189)(116,188)(117,187)(118,186)(119,185)(120,177)(121,176)
(122,182)(123,181)(124,180)(125,179)(126,178)(127,170)(128,169)(129,175)
(130,174)(131,173)(132,172)(133,171)(134,163)(135,162)(136,168)(137,167)
(138,166)(139,165)(140,164)(141,156)(142,155)(143,161)(144,160)(145,159)
(146,158)(147,157);
s1 := Sym(198)!( 1,106)( 2,112)( 3,111)( 4,110)( 5,109)( 6,108)( 7,107)
( 8, 99)( 9,105)( 10,104)( 11,103)( 12,102)( 13,101)( 14,100)( 15,142)
( 16,141)( 17,147)( 18,146)( 19,145)( 20,144)( 21,143)( 22,135)( 23,134)
( 24,140)( 25,139)( 26,138)( 27,137)( 28,136)( 29,128)( 30,127)( 31,133)
( 32,132)( 33,131)( 34,130)( 35,129)( 36,121)( 37,120)( 38,126)( 39,125)
( 40,124)( 41,123)( 42,122)( 43,114)( 44,113)( 45,119)( 46,118)( 47,117)
( 48,116)( 49,115)( 50,155)( 51,161)( 52,160)( 53,159)( 54,158)( 55,157)
( 56,156)( 57,148)( 58,154)( 59,153)( 60,152)( 61,151)( 62,150)( 63,149)
( 64,191)( 65,190)( 66,196)( 67,195)( 68,194)( 69,193)( 70,192)( 71,184)
( 72,183)( 73,189)( 74,188)( 75,187)( 76,186)( 77,185)( 78,177)( 79,176)
( 80,182)( 81,181)( 82,180)( 83,179)( 84,178)( 85,170)( 86,169)( 87,175)
( 88,174)( 89,173)( 90,172)( 91,171)( 92,163)( 93,162)( 94,168)( 95,167)
( 96,166)( 97,165)( 98,164);
s2 := Sym(198)!(197,198);
poly := sub<Sym(198)|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, s1*s2*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*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*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*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*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*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*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*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*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*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*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 >;
to this polytope