Polytope of Type {5,10,4,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,10,4,4}*1600
if this polytope has a name.
Group : SmallGroup(1600,8739)
Rank : 5
Schlafli Type : {5,10,4,4}
Number of vertices, edges, etc : 5, 25, 20, 8, 4
Order of s0s1s2s3s4 : 20
Order of s0s1s2s3s4s3s2s1 : 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 : {5,10,2,4}*800, {5,10,4,2}*800
4-fold quotients : {5,10,2,2}*400
5-fold quotients : {5,2,4,4}*320
10-fold quotients : {5,2,2,4}*160, {5,2,4,2}*160
20-fold quotients : {5,2,2,2}*80
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 5)( 3, 4)( 6, 21)( 7, 25)( 8, 24)( 9, 23)( 10, 22)( 11, 16)
( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 27, 30)( 28, 29)( 31, 46)( 32, 50)
( 33, 49)( 34, 48)( 35, 47)( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)
( 52, 55)( 53, 54)( 56, 71)( 57, 75)( 58, 74)( 59, 73)( 60, 72)( 61, 66)
( 62, 70)( 63, 69)( 64, 68)( 65, 67)( 77, 80)( 78, 79)( 81, 96)( 82,100)
( 83, 99)( 84, 98)( 85, 97)( 86, 91)( 87, 95)( 88, 94)( 89, 93)( 90, 92)
(102,105)(103,104)(106,121)(107,125)(108,124)(109,123)(110,122)(111,116)
(112,120)(113,119)(114,118)(115,117)(127,130)(128,129)(131,146)(132,150)
(133,149)(134,148)(135,147)(136,141)(137,145)(138,144)(139,143)(140,142)
(152,155)(153,154)(156,171)(157,175)(158,174)(159,173)(160,172)(161,166)
(162,170)(163,169)(164,168)(165,167)(177,180)(178,179)(181,196)(182,200)
(183,199)(184,198)(185,197)(186,191)(187,195)(188,194)(189,193)(190,192);;
s1 := ( 1, 7)( 2, 6)( 3, 10)( 4, 9)( 5, 8)( 11, 22)( 12, 21)( 13, 25)
( 14, 24)( 15, 23)( 16, 17)( 18, 20)( 26, 32)( 27, 31)( 28, 35)( 29, 34)
( 30, 33)( 36, 47)( 37, 46)( 38, 50)( 39, 49)( 40, 48)( 41, 42)( 43, 45)
( 51, 57)( 52, 56)( 53, 60)( 54, 59)( 55, 58)( 61, 72)( 62, 71)( 63, 75)
( 64, 74)( 65, 73)( 66, 67)( 68, 70)( 76, 82)( 77, 81)( 78, 85)( 79, 84)
( 80, 83)( 86, 97)( 87, 96)( 88,100)( 89, 99)( 90, 98)( 91, 92)( 93, 95)
(101,107)(102,106)(103,110)(104,109)(105,108)(111,122)(112,121)(113,125)
(114,124)(115,123)(116,117)(118,120)(126,132)(127,131)(128,135)(129,134)
(130,133)(136,147)(137,146)(138,150)(139,149)(140,148)(141,142)(143,145)
(151,157)(152,156)(153,160)(154,159)(155,158)(161,172)(162,171)(163,175)
(164,174)(165,173)(166,167)(168,170)(176,182)(177,181)(178,185)(179,184)
(180,183)(186,197)(187,196)(188,200)(189,199)(190,198)(191,192)(193,195);;
s2 := ( 6, 21)( 7, 22)( 8, 23)( 9, 24)( 10, 25)( 11, 16)( 12, 17)( 13, 18)
( 14, 19)( 15, 20)( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)( 36, 41)
( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 56, 71)( 57, 72)( 58, 73)( 59, 74)
( 60, 75)( 61, 66)( 62, 67)( 63, 68)( 64, 69)( 65, 70)( 81, 96)( 82, 97)
( 83, 98)( 84, 99)( 85,100)( 86, 91)( 87, 92)( 88, 93)( 89, 94)( 90, 95)
(101,126)(102,127)(103,128)(104,129)(105,130)(106,146)(107,147)(108,148)
(109,149)(110,150)(111,141)(112,142)(113,143)(114,144)(115,145)(116,136)
(117,137)(118,138)(119,139)(120,140)(121,131)(122,132)(123,133)(124,134)
(125,135)(151,176)(152,177)(153,178)(154,179)(155,180)(156,196)(157,197)
(158,198)(159,199)(160,200)(161,191)(162,192)(163,193)(164,194)(165,195)
(166,186)(167,187)(168,188)(169,189)(170,190)(171,181)(172,182)(173,183)
(174,184)(175,185);;
s3 := ( 1,101)( 2,102)( 3,103)( 4,104)( 5,105)( 6,106)( 7,107)( 8,108)
( 9,109)( 10,110)( 11,111)( 12,112)( 13,113)( 14,114)( 15,115)( 16,116)
( 17,117)( 18,118)( 19,119)( 20,120)( 21,121)( 22,122)( 23,123)( 24,124)
( 25,125)( 26,126)( 27,127)( 28,128)( 29,129)( 30,130)( 31,131)( 32,132)
( 33,133)( 34,134)( 35,135)( 36,136)( 37,137)( 38,138)( 39,139)( 40,140)
( 41,141)( 42,142)( 43,143)( 44,144)( 45,145)( 46,146)( 47,147)( 48,148)
( 49,149)( 50,150)( 51,151)( 52,152)( 53,153)( 54,154)( 55,155)( 56,156)
( 57,157)( 58,158)( 59,159)( 60,160)( 61,161)( 62,162)( 63,163)( 64,164)
( 65,165)( 66,166)( 67,167)( 68,168)( 69,169)( 70,170)( 71,171)( 72,172)
( 73,173)( 74,174)( 75,175)( 76,176)( 77,177)( 78,178)( 79,179)( 80,180)
( 81,181)( 82,182)( 83,183)( 84,184)( 85,185)( 86,186)( 87,187)( 88,188)
( 89,189)( 90,190)( 91,191)( 92,192)( 93,193)( 94,194)( 95,195)( 96,196)
( 97,197)( 98,198)( 99,199)(100,200);;
s4 := (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,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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(200)!( 2, 5)( 3, 4)( 6, 21)( 7, 25)( 8, 24)( 9, 23)( 10, 22)
( 11, 16)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 27, 30)( 28, 29)( 31, 46)
( 32, 50)( 33, 49)( 34, 48)( 35, 47)( 36, 41)( 37, 45)( 38, 44)( 39, 43)
( 40, 42)( 52, 55)( 53, 54)( 56, 71)( 57, 75)( 58, 74)( 59, 73)( 60, 72)
( 61, 66)( 62, 70)( 63, 69)( 64, 68)( 65, 67)( 77, 80)( 78, 79)( 81, 96)
( 82,100)( 83, 99)( 84, 98)( 85, 97)( 86, 91)( 87, 95)( 88, 94)( 89, 93)
( 90, 92)(102,105)(103,104)(106,121)(107,125)(108,124)(109,123)(110,122)
(111,116)(112,120)(113,119)(114,118)(115,117)(127,130)(128,129)(131,146)
(132,150)(133,149)(134,148)(135,147)(136,141)(137,145)(138,144)(139,143)
(140,142)(152,155)(153,154)(156,171)(157,175)(158,174)(159,173)(160,172)
(161,166)(162,170)(163,169)(164,168)(165,167)(177,180)(178,179)(181,196)
(182,200)(183,199)(184,198)(185,197)(186,191)(187,195)(188,194)(189,193)
(190,192);
s1 := Sym(200)!( 1, 7)( 2, 6)( 3, 10)( 4, 9)( 5, 8)( 11, 22)( 12, 21)
( 13, 25)( 14, 24)( 15, 23)( 16, 17)( 18, 20)( 26, 32)( 27, 31)( 28, 35)
( 29, 34)( 30, 33)( 36, 47)( 37, 46)( 38, 50)( 39, 49)( 40, 48)( 41, 42)
( 43, 45)( 51, 57)( 52, 56)( 53, 60)( 54, 59)( 55, 58)( 61, 72)( 62, 71)
( 63, 75)( 64, 74)( 65, 73)( 66, 67)( 68, 70)( 76, 82)( 77, 81)( 78, 85)
( 79, 84)( 80, 83)( 86, 97)( 87, 96)( 88,100)( 89, 99)( 90, 98)( 91, 92)
( 93, 95)(101,107)(102,106)(103,110)(104,109)(105,108)(111,122)(112,121)
(113,125)(114,124)(115,123)(116,117)(118,120)(126,132)(127,131)(128,135)
(129,134)(130,133)(136,147)(137,146)(138,150)(139,149)(140,148)(141,142)
(143,145)(151,157)(152,156)(153,160)(154,159)(155,158)(161,172)(162,171)
(163,175)(164,174)(165,173)(166,167)(168,170)(176,182)(177,181)(178,185)
(179,184)(180,183)(186,197)(187,196)(188,200)(189,199)(190,198)(191,192)
(193,195);
s2 := Sym(200)!( 6, 21)( 7, 22)( 8, 23)( 9, 24)( 10, 25)( 11, 16)( 12, 17)
( 13, 18)( 14, 19)( 15, 20)( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)
( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 56, 71)( 57, 72)( 58, 73)
( 59, 74)( 60, 75)( 61, 66)( 62, 67)( 63, 68)( 64, 69)( 65, 70)( 81, 96)
( 82, 97)( 83, 98)( 84, 99)( 85,100)( 86, 91)( 87, 92)( 88, 93)( 89, 94)
( 90, 95)(101,126)(102,127)(103,128)(104,129)(105,130)(106,146)(107,147)
(108,148)(109,149)(110,150)(111,141)(112,142)(113,143)(114,144)(115,145)
(116,136)(117,137)(118,138)(119,139)(120,140)(121,131)(122,132)(123,133)
(124,134)(125,135)(151,176)(152,177)(153,178)(154,179)(155,180)(156,196)
(157,197)(158,198)(159,199)(160,200)(161,191)(162,192)(163,193)(164,194)
(165,195)(166,186)(167,187)(168,188)(169,189)(170,190)(171,181)(172,182)
(173,183)(174,184)(175,185);
s3 := Sym(200)!( 1,101)( 2,102)( 3,103)( 4,104)( 5,105)( 6,106)( 7,107)
( 8,108)( 9,109)( 10,110)( 11,111)( 12,112)( 13,113)( 14,114)( 15,115)
( 16,116)( 17,117)( 18,118)( 19,119)( 20,120)( 21,121)( 22,122)( 23,123)
( 24,124)( 25,125)( 26,126)( 27,127)( 28,128)( 29,129)( 30,130)( 31,131)
( 32,132)( 33,133)( 34,134)( 35,135)( 36,136)( 37,137)( 38,138)( 39,139)
( 40,140)( 41,141)( 42,142)( 43,143)( 44,144)( 45,145)( 46,146)( 47,147)
( 48,148)( 49,149)( 50,150)( 51,151)( 52,152)( 53,153)( 54,154)( 55,155)
( 56,156)( 57,157)( 58,158)( 59,159)( 60,160)( 61,161)( 62,162)( 63,163)
( 64,164)( 65,165)( 66,166)( 67,167)( 68,168)( 69,169)( 70,170)( 71,171)
( 72,172)( 73,173)( 74,174)( 75,175)( 76,176)( 77,177)( 78,178)( 79,179)
( 80,180)( 81,181)( 82,182)( 83,183)( 84,184)( 85,185)( 86,186)( 87,187)
( 88,188)( 89,189)( 90,190)( 91,191)( 92,192)( 93,193)( 94,194)( 95,195)
( 96,196)( 97,197)( 98,198)( 99,199)(100,200);
s4 := Sym(200)!(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,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*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope