Polytope of Type {10,4,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,4,4}*1600
Also Known As : {{10,4}4,{4,4|2}}. if this polytope has another name.
Group : SmallGroup(1600,10050)
Rank : 4
Schlafli Type : {10,4,4}
Number of vertices, edges, etc : 50, 100, 40, 4
Order of s0s1s2s3 : 4
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 : {10,4,4}*800, {10,4,2}*800
4-fold quotients : {10,4,2}*400
25-fold quotients : {2,4,4}*64
50-fold quotients : {2,2,4}*32, {2,4,2}*32
100-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,101)( 2,105)( 3,104)( 4,103)( 5,102)( 6,121)( 7,125)( 8,124)
( 9,123)( 10,122)( 11,116)( 12,120)( 13,119)( 14,118)( 15,117)( 16,111)
( 17,115)( 18,114)( 19,113)( 20,112)( 21,106)( 22,110)( 23,109)( 24,108)
( 25,107)( 26,126)( 27,130)( 28,129)( 29,128)( 30,127)( 31,146)( 32,150)
( 33,149)( 34,148)( 35,147)( 36,141)( 37,145)( 38,144)( 39,143)( 40,142)
( 41,136)( 42,140)( 43,139)( 44,138)( 45,137)( 46,131)( 47,135)( 48,134)
( 49,133)( 50,132)( 51,151)( 52,155)( 53,154)( 54,153)( 55,152)( 56,171)
( 57,175)( 58,174)( 59,173)( 60,172)( 61,166)( 62,170)( 63,169)( 64,168)
( 65,167)( 66,161)( 67,165)( 68,164)( 69,163)( 70,162)( 71,156)( 72,160)
( 73,159)( 74,158)( 75,157)( 76,176)( 77,180)( 78,179)( 79,178)( 80,177)
( 81,196)( 82,200)( 83,199)( 84,198)( 85,197)( 86,191)( 87,195)( 88,194)
( 89,193)( 90,192)( 91,186)( 92,190)( 93,189)( 94,188)( 95,187)( 96,181)
( 97,185)( 98,184)( 99,183)(100,182);;
s1 := ( 1, 6)( 2, 17)( 4, 14)( 5, 25)( 7, 12)( 8, 23)( 10, 20)( 11, 21)
( 13, 18)( 19, 24)( 26, 31)( 27, 42)( 29, 39)( 30, 50)( 32, 37)( 33, 48)
( 35, 45)( 36, 46)( 38, 43)( 44, 49)( 51, 56)( 52, 67)( 54, 64)( 55, 75)
( 57, 62)( 58, 73)( 60, 70)( 61, 71)( 63, 68)( 69, 74)( 76, 81)( 77, 92)
( 79, 89)( 80,100)( 82, 87)( 83, 98)( 85, 95)( 86, 96)( 88, 93)( 94, 99)
(101,106)(102,117)(104,114)(105,125)(107,112)(108,123)(110,120)(111,121)
(113,118)(119,124)(126,131)(127,142)(129,139)(130,150)(132,137)(133,148)
(135,145)(136,146)(138,143)(144,149)(151,156)(152,167)(154,164)(155,175)
(157,162)(158,173)(160,170)(161,171)(163,168)(169,174)(176,181)(177,192)
(179,189)(180,200)(182,187)(183,198)(185,195)(186,196)(188,193)(194,199);;
s2 := ( 2, 9)( 3, 12)( 4, 20)( 5, 23)( 6, 13)( 7, 16)( 8, 24)( 11, 25)
( 15, 17)( 19, 21)( 27, 34)( 28, 37)( 29, 45)( 30, 48)( 31, 38)( 32, 41)
( 33, 49)( 36, 50)( 40, 42)( 44, 46)( 51, 76)( 52, 84)( 53, 87)( 54, 95)
( 55, 98)( 56, 88)( 57, 91)( 58, 99)( 59, 77)( 60, 85)( 61,100)( 62, 78)
( 63, 81)( 64, 89)( 65, 92)( 66, 82)( 67, 90)( 68, 93)( 69, 96)( 70, 79)
( 71, 94)( 72, 97)( 73, 80)( 74, 83)( 75, 86)(102,109)(103,112)(104,120)
(105,123)(106,113)(107,116)(108,124)(111,125)(115,117)(119,121)(127,134)
(128,137)(129,145)(130,148)(131,138)(132,141)(133,149)(136,150)(140,142)
(144,146)(151,176)(152,184)(153,187)(154,195)(155,198)(156,188)(157,191)
(158,199)(159,177)(160,185)(161,200)(162,178)(163,181)(164,189)(165,192)
(166,182)(167,190)(168,193)(169,196)(170,179)(171,194)(172,197)(173,180)
(174,183)(175,186);;
s3 := ( 1, 51)( 2, 52)( 3, 53)( 4, 54)( 5, 55)( 6, 56)( 7, 57)( 8, 58)
( 9, 59)( 10, 60)( 11, 61)( 12, 62)( 13, 63)( 14, 64)( 15, 65)( 16, 66)
( 17, 67)( 18, 68)( 19, 69)( 20, 70)( 21, 71)( 22, 72)( 23, 73)( 24, 74)
( 25, 75)( 26, 76)( 27, 77)( 28, 78)( 29, 79)( 30, 80)( 31, 81)( 32, 82)
( 33, 83)( 34, 84)( 35, 85)( 36, 86)( 37, 87)( 38, 88)( 39, 89)( 40, 90)
( 41, 91)( 42, 92)( 43, 93)( 44, 94)( 45, 95)( 46, 96)( 47, 97)( 48, 98)
( 49, 99)( 50,100)(101,151)(102,152)(103,153)(104,154)(105,155)(106,156)
(107,157)(108,158)(109,159)(110,160)(111,161)(112,162)(113,163)(114,164)
(115,165)(116,166)(117,167)(118,168)(119,169)(120,170)(121,171)(122,172)
(123,173)(124,174)(125,175)(126,176)(127,177)(128,178)(129,179)(130,180)
(131,181)(132,182)(133,183)(134,184)(135,185)(136,186)(137,187)(138,188)
(139,189)(140,190)(141,191)(142,192)(143,193)(144,194)(145,195)(146,196)
(147,197)(148,198)(149,199)(150,200);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*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(200)!( 1,101)( 2,105)( 3,104)( 4,103)( 5,102)( 6,121)( 7,125)
( 8,124)( 9,123)( 10,122)( 11,116)( 12,120)( 13,119)( 14,118)( 15,117)
( 16,111)( 17,115)( 18,114)( 19,113)( 20,112)( 21,106)( 22,110)( 23,109)
( 24,108)( 25,107)( 26,126)( 27,130)( 28,129)( 29,128)( 30,127)( 31,146)
( 32,150)( 33,149)( 34,148)( 35,147)( 36,141)( 37,145)( 38,144)( 39,143)
( 40,142)( 41,136)( 42,140)( 43,139)( 44,138)( 45,137)( 46,131)( 47,135)
( 48,134)( 49,133)( 50,132)( 51,151)( 52,155)( 53,154)( 54,153)( 55,152)
( 56,171)( 57,175)( 58,174)( 59,173)( 60,172)( 61,166)( 62,170)( 63,169)
( 64,168)( 65,167)( 66,161)( 67,165)( 68,164)( 69,163)( 70,162)( 71,156)
( 72,160)( 73,159)( 74,158)( 75,157)( 76,176)( 77,180)( 78,179)( 79,178)
( 80,177)( 81,196)( 82,200)( 83,199)( 84,198)( 85,197)( 86,191)( 87,195)
( 88,194)( 89,193)( 90,192)( 91,186)( 92,190)( 93,189)( 94,188)( 95,187)
( 96,181)( 97,185)( 98,184)( 99,183)(100,182);
s1 := Sym(200)!( 1, 6)( 2, 17)( 4, 14)( 5, 25)( 7, 12)( 8, 23)( 10, 20)
( 11, 21)( 13, 18)( 19, 24)( 26, 31)( 27, 42)( 29, 39)( 30, 50)( 32, 37)
( 33, 48)( 35, 45)( 36, 46)( 38, 43)( 44, 49)( 51, 56)( 52, 67)( 54, 64)
( 55, 75)( 57, 62)( 58, 73)( 60, 70)( 61, 71)( 63, 68)( 69, 74)( 76, 81)
( 77, 92)( 79, 89)( 80,100)( 82, 87)( 83, 98)( 85, 95)( 86, 96)( 88, 93)
( 94, 99)(101,106)(102,117)(104,114)(105,125)(107,112)(108,123)(110,120)
(111,121)(113,118)(119,124)(126,131)(127,142)(129,139)(130,150)(132,137)
(133,148)(135,145)(136,146)(138,143)(144,149)(151,156)(152,167)(154,164)
(155,175)(157,162)(158,173)(160,170)(161,171)(163,168)(169,174)(176,181)
(177,192)(179,189)(180,200)(182,187)(183,198)(185,195)(186,196)(188,193)
(194,199);
s2 := Sym(200)!( 2, 9)( 3, 12)( 4, 20)( 5, 23)( 6, 13)( 7, 16)( 8, 24)
( 11, 25)( 15, 17)( 19, 21)( 27, 34)( 28, 37)( 29, 45)( 30, 48)( 31, 38)
( 32, 41)( 33, 49)( 36, 50)( 40, 42)( 44, 46)( 51, 76)( 52, 84)( 53, 87)
( 54, 95)( 55, 98)( 56, 88)( 57, 91)( 58, 99)( 59, 77)( 60, 85)( 61,100)
( 62, 78)( 63, 81)( 64, 89)( 65, 92)( 66, 82)( 67, 90)( 68, 93)( 69, 96)
( 70, 79)( 71, 94)( 72, 97)( 73, 80)( 74, 83)( 75, 86)(102,109)(103,112)
(104,120)(105,123)(106,113)(107,116)(108,124)(111,125)(115,117)(119,121)
(127,134)(128,137)(129,145)(130,148)(131,138)(132,141)(133,149)(136,150)
(140,142)(144,146)(151,176)(152,184)(153,187)(154,195)(155,198)(156,188)
(157,191)(158,199)(159,177)(160,185)(161,200)(162,178)(163,181)(164,189)
(165,192)(166,182)(167,190)(168,193)(169,196)(170,179)(171,194)(172,197)
(173,180)(174,183)(175,186);
s3 := Sym(200)!( 1, 51)( 2, 52)( 3, 53)( 4, 54)( 5, 55)( 6, 56)( 7, 57)
( 8, 58)( 9, 59)( 10, 60)( 11, 61)( 12, 62)( 13, 63)( 14, 64)( 15, 65)
( 16, 66)( 17, 67)( 18, 68)( 19, 69)( 20, 70)( 21, 71)( 22, 72)( 23, 73)
( 24, 74)( 25, 75)( 26, 76)( 27, 77)( 28, 78)( 29, 79)( 30, 80)( 31, 81)
( 32, 82)( 33, 83)( 34, 84)( 35, 85)( 36, 86)( 37, 87)( 38, 88)( 39, 89)
( 40, 90)( 41, 91)( 42, 92)( 43, 93)( 44, 94)( 45, 95)( 46, 96)( 47, 97)
( 48, 98)( 49, 99)( 50,100)(101,151)(102,152)(103,153)(104,154)(105,155)
(106,156)(107,157)(108,158)(109,159)(110,160)(111,161)(112,162)(113,163)
(114,164)(115,165)(116,166)(117,167)(118,168)(119,169)(120,170)(121,171)
(122,172)(123,173)(124,174)(125,175)(126,176)(127,177)(128,178)(129,179)
(130,180)(131,181)(132,182)(133,183)(134,184)(135,185)(136,186)(137,187)
(138,188)(139,189)(140,190)(141,191)(142,192)(143,193)(144,194)(145,195)
(146,196)(147,197)(148,198)(149,199)(150,200);
poly := sub<Sym(200)|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,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope