Polytope of Type {10,4,20}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,4,20}*1600
Also Known As : {{10,4|2},{4,20|2}}. if this polytope has another name.
Group : SmallGroup(1600,7723)
Rank : 4
Schlafli Type : {10,4,20}
Number of vertices, edges, etc : 10, 20, 40, 20
Order of s0s1s2s3 : 20
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 : {10,2,20}*800, {10,4,10}*800
4-fold quotients : {5,2,20}*400, {10,2,10}*400
5-fold quotients : {2,4,20}*320, {10,4,4}*320
8-fold quotients : {5,2,10}*200, {10,2,5}*200
10-fold quotients : {2,2,20}*160, {2,4,10}*160, {10,2,4}*160, {10,4,2}*160
16-fold quotients : {5,2,5}*100
20-fold quotients : {5,2,4}*80, {2,2,10}*80, {10,2,2}*80
25-fold quotients : {2,4,4}*64
40-fold quotients : {2,2,5}*40, {5,2,2}*40
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 := ( 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)
(106,121)(107,122)(108,123)(109,124)(110,125)(111,116)(112,117)(113,118)
(114,119)(115,120)(131,146)(132,147)(133,148)(134,149)(135,150)(136,141)
(137,142)(138,143)(139,144)(140,145)(156,171)(157,172)(158,173)(159,174)
(160,175)(161,166)(162,167)(163,168)(164,169)(165,170)(181,196)(182,197)
(183,198)(184,199)(185,200)(186,191)(187,192)(188,193)(189,194)(190,195);;
s1 := ( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5, 10)( 11, 21)( 12, 22)( 13, 23)
( 14, 24)( 15, 25)( 26, 31)( 27, 32)( 28, 33)( 29, 34)( 30, 35)( 36, 46)
( 37, 47)( 38, 48)( 39, 49)( 40, 50)( 51, 56)( 52, 57)( 53, 58)( 54, 59)
( 55, 60)( 61, 71)( 62, 72)( 63, 73)( 64, 74)( 65, 75)( 76, 81)( 77, 82)
( 78, 83)( 79, 84)( 80, 85)( 86, 96)( 87, 97)( 88, 98)( 89, 99)( 90,100)
(101,156)(102,157)(103,158)(104,159)(105,160)(106,151)(107,152)(108,153)
(109,154)(110,155)(111,171)(112,172)(113,173)(114,174)(115,175)(116,166)
(117,167)(118,168)(119,169)(120,170)(121,161)(122,162)(123,163)(124,164)
(125,165)(126,181)(127,182)(128,183)(129,184)(130,185)(131,176)(132,177)
(133,178)(134,179)(135,180)(136,196)(137,197)(138,198)(139,199)(140,200)
(141,191)(142,192)(143,193)(144,194)(145,195)(146,186)(147,187)(148,188)
(149,189)(150,190);;
s2 := ( 1,101)( 2,105)( 3,104)( 4,103)( 5,102)( 6,106)( 7,110)( 8,109)
( 9,108)( 10,107)( 11,111)( 12,115)( 13,114)( 14,113)( 15,112)( 16,116)
( 17,120)( 18,119)( 19,118)( 20,117)( 21,121)( 22,125)( 23,124)( 24,123)
( 25,122)( 26,126)( 27,130)( 28,129)( 29,128)( 30,127)( 31,131)( 32,135)
( 33,134)( 34,133)( 35,132)( 36,136)( 37,140)( 38,139)( 39,138)( 40,137)
( 41,141)( 42,145)( 43,144)( 44,143)( 45,142)( 46,146)( 47,150)( 48,149)
( 49,148)( 50,147)( 51,151)( 52,155)( 53,154)( 54,153)( 55,152)( 56,156)
( 57,160)( 58,159)( 59,158)( 60,157)( 61,161)( 62,165)( 63,164)( 64,163)
( 65,162)( 66,166)( 67,170)( 68,169)( 69,168)( 70,167)( 71,171)( 72,175)
( 73,174)( 74,173)( 75,172)( 76,176)( 77,180)( 78,179)( 79,178)( 80,177)
( 81,181)( 82,185)( 83,184)( 84,183)( 85,182)( 86,186)( 87,190)( 88,189)
( 89,188)( 90,187)( 91,191)( 92,195)( 93,194)( 94,193)( 95,192)( 96,196)
( 97,200)( 98,199)( 99,198)(100,197);;
s3 := ( 1, 2)( 3, 5)( 6, 7)( 8, 10)( 11, 12)( 13, 15)( 16, 17)( 18, 20)
( 21, 22)( 23, 25)( 26, 27)( 28, 30)( 31, 32)( 33, 35)( 36, 37)( 38, 40)
( 41, 42)( 43, 45)( 46, 47)( 48, 50)( 51, 52)( 53, 55)( 56, 57)( 58, 60)
( 61, 62)( 63, 65)( 66, 67)( 68, 70)( 71, 72)( 73, 75)( 76, 77)( 78, 80)
( 81, 82)( 83, 85)( 86, 87)( 88, 90)( 91, 92)( 93, 95)( 96, 97)( 98,100)
(101,127)(102,126)(103,130)(104,129)(105,128)(106,132)(107,131)(108,135)
(109,134)(110,133)(111,137)(112,136)(113,140)(114,139)(115,138)(116,142)
(117,141)(118,145)(119,144)(120,143)(121,147)(122,146)(123,150)(124,149)
(125,148)(151,177)(152,176)(153,180)(154,179)(155,178)(156,182)(157,181)
(158,185)(159,184)(160,183)(161,187)(162,186)(163,190)(164,189)(165,188)
(166,192)(167,191)(168,195)(169,194)(170,193)(171,197)(172,196)(173,200)
(174,199)(175,198);;
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*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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)!( 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)(106,121)(107,122)(108,123)(109,124)(110,125)(111,116)(112,117)
(113,118)(114,119)(115,120)(131,146)(132,147)(133,148)(134,149)(135,150)
(136,141)(137,142)(138,143)(139,144)(140,145)(156,171)(157,172)(158,173)
(159,174)(160,175)(161,166)(162,167)(163,168)(164,169)(165,170)(181,196)
(182,197)(183,198)(184,199)(185,200)(186,191)(187,192)(188,193)(189,194)
(190,195);
s1 := Sym(200)!( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5, 10)( 11, 21)( 12, 22)
( 13, 23)( 14, 24)( 15, 25)( 26, 31)( 27, 32)( 28, 33)( 29, 34)( 30, 35)
( 36, 46)( 37, 47)( 38, 48)( 39, 49)( 40, 50)( 51, 56)( 52, 57)( 53, 58)
( 54, 59)( 55, 60)( 61, 71)( 62, 72)( 63, 73)( 64, 74)( 65, 75)( 76, 81)
( 77, 82)( 78, 83)( 79, 84)( 80, 85)( 86, 96)( 87, 97)( 88, 98)( 89, 99)
( 90,100)(101,156)(102,157)(103,158)(104,159)(105,160)(106,151)(107,152)
(108,153)(109,154)(110,155)(111,171)(112,172)(113,173)(114,174)(115,175)
(116,166)(117,167)(118,168)(119,169)(120,170)(121,161)(122,162)(123,163)
(124,164)(125,165)(126,181)(127,182)(128,183)(129,184)(130,185)(131,176)
(132,177)(133,178)(134,179)(135,180)(136,196)(137,197)(138,198)(139,199)
(140,200)(141,191)(142,192)(143,193)(144,194)(145,195)(146,186)(147,187)
(148,188)(149,189)(150,190);
s2 := Sym(200)!( 1,101)( 2,105)( 3,104)( 4,103)( 5,102)( 6,106)( 7,110)
( 8,109)( 9,108)( 10,107)( 11,111)( 12,115)( 13,114)( 14,113)( 15,112)
( 16,116)( 17,120)( 18,119)( 19,118)( 20,117)( 21,121)( 22,125)( 23,124)
( 24,123)( 25,122)( 26,126)( 27,130)( 28,129)( 29,128)( 30,127)( 31,131)
( 32,135)( 33,134)( 34,133)( 35,132)( 36,136)( 37,140)( 38,139)( 39,138)
( 40,137)( 41,141)( 42,145)( 43,144)( 44,143)( 45,142)( 46,146)( 47,150)
( 48,149)( 49,148)( 50,147)( 51,151)( 52,155)( 53,154)( 54,153)( 55,152)
( 56,156)( 57,160)( 58,159)( 59,158)( 60,157)( 61,161)( 62,165)( 63,164)
( 64,163)( 65,162)( 66,166)( 67,170)( 68,169)( 69,168)( 70,167)( 71,171)
( 72,175)( 73,174)( 74,173)( 75,172)( 76,176)( 77,180)( 78,179)( 79,178)
( 80,177)( 81,181)( 82,185)( 83,184)( 84,183)( 85,182)( 86,186)( 87,190)
( 88,189)( 89,188)( 90,187)( 91,191)( 92,195)( 93,194)( 94,193)( 95,192)
( 96,196)( 97,200)( 98,199)( 99,198)(100,197);
s3 := Sym(200)!( 1, 2)( 3, 5)( 6, 7)( 8, 10)( 11, 12)( 13, 15)( 16, 17)
( 18, 20)( 21, 22)( 23, 25)( 26, 27)( 28, 30)( 31, 32)( 33, 35)( 36, 37)
( 38, 40)( 41, 42)( 43, 45)( 46, 47)( 48, 50)( 51, 52)( 53, 55)( 56, 57)
( 58, 60)( 61, 62)( 63, 65)( 66, 67)( 68, 70)( 71, 72)( 73, 75)( 76, 77)
( 78, 80)( 81, 82)( 83, 85)( 86, 87)( 88, 90)( 91, 92)( 93, 95)( 96, 97)
( 98,100)(101,127)(102,126)(103,130)(104,129)(105,128)(106,132)(107,131)
(108,135)(109,134)(110,133)(111,137)(112,136)(113,140)(114,139)(115,138)
(116,142)(117,141)(118,145)(119,144)(120,143)(121,147)(122,146)(123,150)
(124,149)(125,148)(151,177)(152,176)(153,180)(154,179)(155,178)(156,182)
(157,181)(158,185)(159,184)(160,183)(161,187)(162,186)(163,190)(164,189)
(165,188)(166,192)(167,191)(168,195)(169,194)(170,193)(171,197)(172,196)
(173,200)(174,199)(175,198);
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*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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