Polytope of Type {10,10,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,10,4}*800c
if this polytope has a name.
Group : SmallGroup(800,1153)
Rank : 4
Schlafli Type : {10,10,4}
Number of vertices, edges, etc : 10, 50, 20, 4
Order of s0s1s2s3 : 20
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{10,10,4,2} of size 1600
Vertex Figure Of :
{2,10,10,4} of size 1600
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {5,10,4}*400, {10,10,2}*400c
4-fold quotients : {5,10,2}*200
5-fold quotients : {10,2,4}*160
10-fold quotients : {5,2,4}*80, {10,2,2}*80
20-fold quotients : {5,2,2}*40
25-fold quotients : {2,2,4}*32
50-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {20,10,4}*1600b, {10,10,8}*1600c, {10,20,4}*1600c
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 := ( 1,107)( 2,106)( 3,110)( 4,109)( 5,108)( 6,102)( 7,101)( 8,105)
( 9,104)( 10,103)( 11,122)( 12,121)( 13,125)( 14,124)( 15,123)( 16,117)
( 17,116)( 18,120)( 19,119)( 20,118)( 21,112)( 22,111)( 23,115)( 24,114)
( 25,113)( 26,132)( 27,131)( 28,135)( 29,134)( 30,133)( 31,127)( 32,126)
( 33,130)( 34,129)( 35,128)( 36,147)( 37,146)( 38,150)( 39,149)( 40,148)
( 41,142)( 42,141)( 43,145)( 44,144)( 45,143)( 46,137)( 47,136)( 48,140)
( 49,139)( 50,138)( 51,157)( 52,156)( 53,160)( 54,159)( 55,158)( 56,152)
( 57,151)( 58,155)( 59,154)( 60,153)( 61,172)( 62,171)( 63,175)( 64,174)
( 65,173)( 66,167)( 67,166)( 68,170)( 69,169)( 70,168)( 71,162)( 72,161)
( 73,165)( 74,164)( 75,163)( 76,182)( 77,181)( 78,185)( 79,184)( 80,183)
( 81,177)( 82,176)( 83,180)( 84,179)( 85,178)( 86,197)( 87,196)( 88,200)
( 89,199)( 90,198)( 91,192)( 92,191)( 93,195)( 94,194)( 95,193)( 96,187)
( 97,186)( 98,190)( 99,189)(100,188);;
s2 := ( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)
( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)( 38, 39)
( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 51, 76)( 52, 80)( 53, 79)( 54, 78)
( 55, 77)( 56, 81)( 57, 85)( 58, 84)( 59, 83)( 60, 82)( 61, 86)( 62, 90)
( 63, 89)( 64, 88)( 65, 87)( 66, 91)( 67, 95)( 68, 94)( 69, 93)( 70, 92)
( 71, 96)( 72,100)( 73, 99)( 74, 98)( 75, 97)(102,105)(103,104)(107,110)
(108,109)(112,115)(113,114)(117,120)(118,119)(122,125)(123,124)(127,130)
(128,129)(132,135)(133,134)(137,140)(138,139)(142,145)(143,144)(147,150)
(148,149)(151,176)(152,180)(153,179)(154,178)(155,177)(156,181)(157,185)
(158,184)(159,183)(160,182)(161,186)(162,190)(163,189)(164,188)(165,187)
(166,191)(167,195)(168,194)(169,193)(170,192)(171,196)(172,200)(173,199)
(174,198)(175,197);;
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*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*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)!( 1,107)( 2,106)( 3,110)( 4,109)( 5,108)( 6,102)( 7,101)
( 8,105)( 9,104)( 10,103)( 11,122)( 12,121)( 13,125)( 14,124)( 15,123)
( 16,117)( 17,116)( 18,120)( 19,119)( 20,118)( 21,112)( 22,111)( 23,115)
( 24,114)( 25,113)( 26,132)( 27,131)( 28,135)( 29,134)( 30,133)( 31,127)
( 32,126)( 33,130)( 34,129)( 35,128)( 36,147)( 37,146)( 38,150)( 39,149)
( 40,148)( 41,142)( 42,141)( 43,145)( 44,144)( 45,143)( 46,137)( 47,136)
( 48,140)( 49,139)( 50,138)( 51,157)( 52,156)( 53,160)( 54,159)( 55,158)
( 56,152)( 57,151)( 58,155)( 59,154)( 60,153)( 61,172)( 62,171)( 63,175)
( 64,174)( 65,173)( 66,167)( 67,166)( 68,170)( 69,169)( 70,168)( 71,162)
( 72,161)( 73,165)( 74,164)( 75,163)( 76,182)( 77,181)( 78,185)( 79,184)
( 80,183)( 81,177)( 82,176)( 83,180)( 84,179)( 85,178)( 86,197)( 87,196)
( 88,200)( 89,199)( 90,198)( 91,192)( 92,191)( 93,195)( 94,194)( 95,193)
( 96,187)( 97,186)( 98,190)( 99,189)(100,188);
s2 := Sym(200)!( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)
( 18, 19)( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)
( 38, 39)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 51, 76)( 52, 80)( 53, 79)
( 54, 78)( 55, 77)( 56, 81)( 57, 85)( 58, 84)( 59, 83)( 60, 82)( 61, 86)
( 62, 90)( 63, 89)( 64, 88)( 65, 87)( 66, 91)( 67, 95)( 68, 94)( 69, 93)
( 70, 92)( 71, 96)( 72,100)( 73, 99)( 74, 98)( 75, 97)(102,105)(103,104)
(107,110)(108,109)(112,115)(113,114)(117,120)(118,119)(122,125)(123,124)
(127,130)(128,129)(132,135)(133,134)(137,140)(138,139)(142,145)(143,144)
(147,150)(148,149)(151,176)(152,180)(153,179)(154,178)(155,177)(156,181)
(157,185)(158,184)(159,183)(160,182)(161,186)(162,190)(163,189)(164,188)
(165,187)(166,191)(167,195)(168,194)(169,193)(170,192)(171,196)(172,200)
(173,199)(174,198)(175,197);
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*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope