Polytope of Type {5,10,6,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,10,6,3}*1800
if this polytope has a name.
Group : SmallGroup(1800,681)
Rank : 5
Schlafli Type : {5,10,6,3}
Number of vertices, edges, etc : 5, 25, 30, 9, 3
Order of s0s1s2s3s4 : 30
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) :
3-fold quotients : {5,10,2,3}*600
5-fold quotients : {5,2,6,3}*360
15-fold quotients : {5,2,2,3}*120
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)
(202,205)(203,204)(206,221)(207,225)(208,224)(209,223)(210,222)(211,216)
(212,220)(213,219)(214,218)(215,217);;
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)
(201,207)(202,206)(203,210)(204,209)(205,208)(211,222)(212,221)(213,225)
(214,224)(215,223)(216,217)(218,220);;
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)( 76,151)( 77,152)
( 78,153)( 79,154)( 80,155)( 81,171)( 82,172)( 83,173)( 84,174)( 85,175)
( 86,166)( 87,167)( 88,168)( 89,169)( 90,170)( 91,161)( 92,162)( 93,163)
( 94,164)( 95,165)( 96,156)( 97,157)( 98,158)( 99,159)(100,160)(101,176)
(102,177)(103,178)(104,179)(105,180)(106,196)(107,197)(108,198)(109,199)
(110,200)(111,191)(112,192)(113,193)(114,194)(115,195)(116,186)(117,187)
(118,188)(119,189)(120,190)(121,181)(122,182)(123,183)(124,184)(125,185)
(126,201)(127,202)(128,203)(129,204)(130,205)(131,221)(132,222)(133,223)
(134,224)(135,225)(136,216)(137,217)(138,218)(139,219)(140,220)(141,211)
(142,212)(143,213)(144,214)(145,215)(146,206)(147,207)(148,208)(149,209)
(150,210);;
s3 := ( 1, 76)( 2, 77)( 3, 78)( 4, 79)( 5, 80)( 6, 81)( 7, 82)( 8, 83)
( 9, 84)( 10, 85)( 11, 86)( 12, 87)( 13, 88)( 14, 89)( 15, 90)( 16, 91)
( 17, 92)( 18, 93)( 19, 94)( 20, 95)( 21, 96)( 22, 97)( 23, 98)( 24, 99)
( 25,100)( 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)( 51,101)( 52,102)( 53,103)( 54,104)( 55,105)( 56,106)
( 57,107)( 58,108)( 59,109)( 60,110)( 61,111)( 62,112)( 63,113)( 64,114)
( 65,115)( 66,116)( 67,117)( 68,118)( 69,119)( 70,120)( 71,121)( 72,122)
( 73,123)( 74,124)( 75,125)(176,201)(177,202)(178,203)(179,204)(180,205)
(181,206)(182,207)(183,208)(184,209)(185,210)(186,211)(187,212)(188,213)
(189,214)(190,215)(191,216)(192,217)(193,218)(194,219)(195,220)(196,221)
(197,222)(198,223)(199,224)(200,225);;
s4 := ( 1, 26)( 2, 27)( 3, 28)( 4, 29)( 5, 30)( 6, 31)( 7, 32)( 8, 33)
( 9, 34)( 10, 35)( 11, 36)( 12, 37)( 13, 38)( 14, 39)( 15, 40)( 16, 41)
( 17, 42)( 18, 43)( 19, 44)( 20, 45)( 21, 46)( 22, 47)( 23, 48)( 24, 49)
( 25, 50)( 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)(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)(126,201)(127,202)(128,203)(129,204)(130,205)
(131,206)(132,207)(133,208)(134,209)(135,210)(136,211)(137,212)(138,213)
(139,214)(140,215)(141,216)(142,217)(143,218)(144,219)(145,220)(146,221)
(147,222)(148,223)(149,224)(150,225);;
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, s3*s4*s3*s4*s3*s4,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(225)!( 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)(202,205)(203,204)(206,221)(207,225)(208,224)(209,223)(210,222)
(211,216)(212,220)(213,219)(214,218)(215,217);
s1 := Sym(225)!( 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)(201,207)(202,206)(203,210)(204,209)(205,208)(211,222)(212,221)
(213,225)(214,224)(215,223)(216,217)(218,220);
s2 := Sym(225)!( 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)( 76,151)
( 77,152)( 78,153)( 79,154)( 80,155)( 81,171)( 82,172)( 83,173)( 84,174)
( 85,175)( 86,166)( 87,167)( 88,168)( 89,169)( 90,170)( 91,161)( 92,162)
( 93,163)( 94,164)( 95,165)( 96,156)( 97,157)( 98,158)( 99,159)(100,160)
(101,176)(102,177)(103,178)(104,179)(105,180)(106,196)(107,197)(108,198)
(109,199)(110,200)(111,191)(112,192)(113,193)(114,194)(115,195)(116,186)
(117,187)(118,188)(119,189)(120,190)(121,181)(122,182)(123,183)(124,184)
(125,185)(126,201)(127,202)(128,203)(129,204)(130,205)(131,221)(132,222)
(133,223)(134,224)(135,225)(136,216)(137,217)(138,218)(139,219)(140,220)
(141,211)(142,212)(143,213)(144,214)(145,215)(146,206)(147,207)(148,208)
(149,209)(150,210);
s3 := Sym(225)!( 1, 76)( 2, 77)( 3, 78)( 4, 79)( 5, 80)( 6, 81)( 7, 82)
( 8, 83)( 9, 84)( 10, 85)( 11, 86)( 12, 87)( 13, 88)( 14, 89)( 15, 90)
( 16, 91)( 17, 92)( 18, 93)( 19, 94)( 20, 95)( 21, 96)( 22, 97)( 23, 98)
( 24, 99)( 25,100)( 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)( 51,101)( 52,102)( 53,103)( 54,104)( 55,105)
( 56,106)( 57,107)( 58,108)( 59,109)( 60,110)( 61,111)( 62,112)( 63,113)
( 64,114)( 65,115)( 66,116)( 67,117)( 68,118)( 69,119)( 70,120)( 71,121)
( 72,122)( 73,123)( 74,124)( 75,125)(176,201)(177,202)(178,203)(179,204)
(180,205)(181,206)(182,207)(183,208)(184,209)(185,210)(186,211)(187,212)
(188,213)(189,214)(190,215)(191,216)(192,217)(193,218)(194,219)(195,220)
(196,221)(197,222)(198,223)(199,224)(200,225);
s4 := Sym(225)!( 1, 26)( 2, 27)( 3, 28)( 4, 29)( 5, 30)( 6, 31)( 7, 32)
( 8, 33)( 9, 34)( 10, 35)( 11, 36)( 12, 37)( 13, 38)( 14, 39)( 15, 40)
( 16, 41)( 17, 42)( 18, 43)( 19, 44)( 20, 45)( 21, 46)( 22, 47)( 23, 48)
( 24, 49)( 25, 50)( 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)(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)(126,201)(127,202)(128,203)(129,204)
(130,205)(131,206)(132,207)(133,208)(134,209)(135,210)(136,211)(137,212)
(138,213)(139,214)(140,215)(141,216)(142,217)(143,218)(144,219)(145,220)
(146,221)(147,222)(148,223)(149,224)(150,225);
poly := sub<Sym(225)|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, s3*s4*s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s4*s2*s3*s2*s3*s4*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope