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