Polytope of Type {194}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {194}*388
Also Known As : 194-gon, {194}. if this polytope has another name.
Group : SmallGroup(388,4)
Rank : 2
Schlafli Type : {194}
Number of vertices, edges, etc : 194, 194
Order of s0s1 : 194
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{194,2} of size 776
{194,4} of size 1552
Vertex Figure Of :
{2,194} of size 776
{4,194} of size 1552
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {97}*194
97-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
2-fold covers : {388}*776
3-fold covers : {582}*1164
4-fold covers : {776}*1552
5-fold covers : {970}*1940
Permutation Representation (GAP) :
s0 := ( 2, 97)( 3, 96)( 4, 95)( 5, 94)( 6, 93)( 7, 92)( 8, 91)( 9, 90)
( 10, 89)( 11, 88)( 12, 87)( 13, 86)( 14, 85)( 15, 84)( 16, 83)( 17, 82)
( 18, 81)( 19, 80)( 20, 79)( 21, 78)( 22, 77)( 23, 76)( 24, 75)( 25, 74)
( 26, 73)( 27, 72)( 28, 71)( 29, 70)( 30, 69)( 31, 68)( 32, 67)( 33, 66)
( 34, 65)( 35, 64)( 36, 63)( 37, 62)( 38, 61)( 39, 60)( 40, 59)( 41, 58)
( 42, 57)( 43, 56)( 44, 55)( 45, 54)( 46, 53)( 47, 52)( 48, 51)( 49, 50)
( 99,194)(100,193)(101,192)(102,191)(103,190)(104,189)(105,188)(106,187)
(107,186)(108,185)(109,184)(110,183)(111,182)(112,181)(113,180)(114,179)
(115,178)(116,177)(117,176)(118,175)(119,174)(120,173)(121,172)(122,171)
(123,170)(124,169)(125,168)(126,167)(127,166)(128,165)(129,164)(130,163)
(131,162)(132,161)(133,160)(134,159)(135,158)(136,157)(137,156)(138,155)
(139,154)(140,153)(141,152)(142,151)(143,150)(144,149)(145,148)(146,147);;
s1 := ( 1, 99)( 2, 98)( 3,194)( 4,193)( 5,192)( 6,191)( 7,190)( 8,189)
( 9,188)( 10,187)( 11,186)( 12,185)( 13,184)( 14,183)( 15,182)( 16,181)
( 17,180)( 18,179)( 19,178)( 20,177)( 21,176)( 22,175)( 23,174)( 24,173)
( 25,172)( 26,171)( 27,170)( 28,169)( 29,168)( 30,167)( 31,166)( 32,165)
( 33,164)( 34,163)( 35,162)( 36,161)( 37,160)( 38,159)( 39,158)( 40,157)
( 41,156)( 42,155)( 43,154)( 44,153)( 45,152)( 46,151)( 47,150)( 48,149)
( 49,148)( 50,147)( 51,146)( 52,145)( 53,144)( 54,143)( 55,142)( 56,141)
( 57,140)( 58,139)( 59,138)( 60,137)( 61,136)( 62,135)( 63,134)( 64,133)
( 65,132)( 66,131)( 67,130)( 68,129)( 69,128)( 70,127)( 71,126)( 72,125)
( 73,124)( 74,123)( 75,122)( 76,121)( 77,120)( 78,119)( 79,118)( 80,117)
( 81,116)( 82,115)( 83,114)( 84,113)( 85,112)( 86,111)( 87,110)( 88,109)
( 89,108)( 90,107)( 91,106)( 92,105)( 93,104)( 94,103)( 95,102)( 96,101)
( 97,100);;
poly := Group([s0,s1]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1");;
s0 := F.1;; s1 := F.2;;
rels := [ s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(194)!( 2, 97)( 3, 96)( 4, 95)( 5, 94)( 6, 93)( 7, 92)( 8, 91)
( 9, 90)( 10, 89)( 11, 88)( 12, 87)( 13, 86)( 14, 85)( 15, 84)( 16, 83)
( 17, 82)( 18, 81)( 19, 80)( 20, 79)( 21, 78)( 22, 77)( 23, 76)( 24, 75)
( 25, 74)( 26, 73)( 27, 72)( 28, 71)( 29, 70)( 30, 69)( 31, 68)( 32, 67)
( 33, 66)( 34, 65)( 35, 64)( 36, 63)( 37, 62)( 38, 61)( 39, 60)( 40, 59)
( 41, 58)( 42, 57)( 43, 56)( 44, 55)( 45, 54)( 46, 53)( 47, 52)( 48, 51)
( 49, 50)( 99,194)(100,193)(101,192)(102,191)(103,190)(104,189)(105,188)
(106,187)(107,186)(108,185)(109,184)(110,183)(111,182)(112,181)(113,180)
(114,179)(115,178)(116,177)(117,176)(118,175)(119,174)(120,173)(121,172)
(122,171)(123,170)(124,169)(125,168)(126,167)(127,166)(128,165)(129,164)
(130,163)(131,162)(132,161)(133,160)(134,159)(135,158)(136,157)(137,156)
(138,155)(139,154)(140,153)(141,152)(142,151)(143,150)(144,149)(145,148)
(146,147);
s1 := Sym(194)!( 1, 99)( 2, 98)( 3,194)( 4,193)( 5,192)( 6,191)( 7,190)
( 8,189)( 9,188)( 10,187)( 11,186)( 12,185)( 13,184)( 14,183)( 15,182)
( 16,181)( 17,180)( 18,179)( 19,178)( 20,177)( 21,176)( 22,175)( 23,174)
( 24,173)( 25,172)( 26,171)( 27,170)( 28,169)( 29,168)( 30,167)( 31,166)
( 32,165)( 33,164)( 34,163)( 35,162)( 36,161)( 37,160)( 38,159)( 39,158)
( 40,157)( 41,156)( 42,155)( 43,154)( 44,153)( 45,152)( 46,151)( 47,150)
( 48,149)( 49,148)( 50,147)( 51,146)( 52,145)( 53,144)( 54,143)( 55,142)
( 56,141)( 57,140)( 58,139)( 59,138)( 60,137)( 61,136)( 62,135)( 63,134)
( 64,133)( 65,132)( 66,131)( 67,130)( 68,129)( 69,128)( 70,127)( 71,126)
( 72,125)( 73,124)( 74,123)( 75,122)( 76,121)( 77,120)( 78,119)( 79,118)
( 80,117)( 81,116)( 82,115)( 83,114)( 84,113)( 85,112)( 86,111)( 87,110)
( 88,109)( 89,108)( 90,107)( 91,106)( 92,105)( 93,104)( 94,103)( 95,102)
( 96,101)( 97,100);
poly := sub<Sym(194)|s0,s1>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
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