Polytope of Type {6,100}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,100}*1200a
Also Known As : {6,100|2}. if this polytope has another name.
Group : SmallGroup(1200,131)
Rank : 3
Schlafli Type : {6,100}
Number of vertices, edges, etc : 6, 300, 100
Order of s0s1s2 : 300
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
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 : {6,50}*600
3-fold quotients : {2,100}*400
5-fold quotients : {6,20}*240a
6-fold quotients : {2,50}*200
10-fold quotients : {6,10}*120
12-fold quotients : {2,25}*100
15-fold quotients : {2,20}*80
25-fold quotients : {6,4}*48a
30-fold quotients : {2,10}*40
50-fold quotients : {6,2}*24
60-fold quotients : {2,5}*20
75-fold quotients : {2,4}*16
100-fold quotients : {3,2}*12
150-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 26, 51)( 27, 52)( 28, 53)( 29, 54)( 30, 55)( 31, 56)( 32, 57)( 33, 58)
( 34, 59)( 35, 60)( 36, 61)( 37, 62)( 38, 63)( 39, 64)( 40, 65)( 41, 66)
( 42, 67)( 43, 68)( 44, 69)( 45, 70)( 46, 71)( 47, 72)( 48, 73)( 49, 74)
( 50, 75)(101,126)(102,127)(103,128)(104,129)(105,130)(106,131)(107,132)
(108,133)(109,134)(110,135)(111,136)(112,137)(113,138)(114,139)(115,140)
(116,141)(117,142)(118,143)(119,144)(120,145)(121,146)(122,147)(123,148)
(124,149)(125,150)(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)(251,276)(252,277)(253,278)(254,279)(255,280)
(256,281)(257,282)(258,283)(259,284)(260,285)(261,286)(262,287)(263,288)
(264,289)(265,290)(266,291)(267,292)(268,293)(269,294)(270,295)(271,296)
(272,297)(273,298)(274,299)(275,300);;
s1 := ( 1, 26)( 2, 30)( 3, 29)( 4, 28)( 5, 27)( 6, 50)( 7, 49)( 8, 48)
( 9, 47)( 10, 46)( 11, 45)( 12, 44)( 13, 43)( 14, 42)( 15, 41)( 16, 40)
( 17, 39)( 18, 38)( 19, 37)( 20, 36)( 21, 35)( 22, 34)( 23, 33)( 24, 32)
( 25, 31)( 52, 55)( 53, 54)( 56, 75)( 57, 74)( 58, 73)( 59, 72)( 60, 71)
( 61, 70)( 62, 69)( 63, 68)( 64, 67)( 65, 66)( 76,101)( 77,105)( 78,104)
( 79,103)( 80,102)( 81,125)( 82,124)( 83,123)( 84,122)( 85,121)( 86,120)
( 87,119)( 88,118)( 89,117)( 90,116)( 91,115)( 92,114)( 93,113)( 94,112)
( 95,111)( 96,110)( 97,109)( 98,108)( 99,107)(100,106)(127,130)(128,129)
(131,150)(132,149)(133,148)(134,147)(135,146)(136,145)(137,144)(138,143)
(139,142)(140,141)(151,251)(152,255)(153,254)(154,253)(155,252)(156,275)
(157,274)(158,273)(159,272)(160,271)(161,270)(162,269)(163,268)(164,267)
(165,266)(166,265)(167,264)(168,263)(169,262)(170,261)(171,260)(172,259)
(173,258)(174,257)(175,256)(176,226)(177,230)(178,229)(179,228)(180,227)
(181,250)(182,249)(183,248)(184,247)(185,246)(186,245)(187,244)(188,243)
(189,242)(190,241)(191,240)(192,239)(193,238)(194,237)(195,236)(196,235)
(197,234)(198,233)(199,232)(200,231)(201,276)(202,280)(203,279)(204,278)
(205,277)(206,300)(207,299)(208,298)(209,297)(210,296)(211,295)(212,294)
(213,293)(214,292)(215,291)(216,290)(217,289)(218,288)(219,287)(220,286)
(221,285)(222,284)(223,283)(224,282)(225,281);;
s2 := ( 1,156)( 2,160)( 3,159)( 4,158)( 5,157)( 6,151)( 7,155)( 8,154)
( 9,153)( 10,152)( 11,175)( 12,174)( 13,173)( 14,172)( 15,171)( 16,170)
( 17,169)( 18,168)( 19,167)( 20,166)( 21,165)( 22,164)( 23,163)( 24,162)
( 25,161)( 26,181)( 27,185)( 28,184)( 29,183)( 30,182)( 31,176)( 32,180)
( 33,179)( 34,178)( 35,177)( 36,200)( 37,199)( 38,198)( 39,197)( 40,196)
( 41,195)( 42,194)( 43,193)( 44,192)( 45,191)( 46,190)( 47,189)( 48,188)
( 49,187)( 50,186)( 51,206)( 52,210)( 53,209)( 54,208)( 55,207)( 56,201)
( 57,205)( 58,204)( 59,203)( 60,202)( 61,225)( 62,224)( 63,223)( 64,222)
( 65,221)( 66,220)( 67,219)( 68,218)( 69,217)( 70,216)( 71,215)( 72,214)
( 73,213)( 74,212)( 75,211)( 76,231)( 77,235)( 78,234)( 79,233)( 80,232)
( 81,226)( 82,230)( 83,229)( 84,228)( 85,227)( 86,250)( 87,249)( 88,248)
( 89,247)( 90,246)( 91,245)( 92,244)( 93,243)( 94,242)( 95,241)( 96,240)
( 97,239)( 98,238)( 99,237)(100,236)(101,256)(102,260)(103,259)(104,258)
(105,257)(106,251)(107,255)(108,254)(109,253)(110,252)(111,275)(112,274)
(113,273)(114,272)(115,271)(116,270)(117,269)(118,268)(119,267)(120,266)
(121,265)(122,264)(123,263)(124,262)(125,261)(126,281)(127,285)(128,284)
(129,283)(130,282)(131,276)(132,280)(133,279)(134,278)(135,277)(136,300)
(137,299)(138,298)(139,297)(140,296)(141,295)(142,294)(143,293)(144,292)
(145,291)(146,290)(147,289)(148,288)(149,287)(150,286);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(300)!( 26, 51)( 27, 52)( 28, 53)( 29, 54)( 30, 55)( 31, 56)( 32, 57)
( 33, 58)( 34, 59)( 35, 60)( 36, 61)( 37, 62)( 38, 63)( 39, 64)( 40, 65)
( 41, 66)( 42, 67)( 43, 68)( 44, 69)( 45, 70)( 46, 71)( 47, 72)( 48, 73)
( 49, 74)( 50, 75)(101,126)(102,127)(103,128)(104,129)(105,130)(106,131)
(107,132)(108,133)(109,134)(110,135)(111,136)(112,137)(113,138)(114,139)
(115,140)(116,141)(117,142)(118,143)(119,144)(120,145)(121,146)(122,147)
(123,148)(124,149)(125,150)(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)(251,276)(252,277)(253,278)(254,279)
(255,280)(256,281)(257,282)(258,283)(259,284)(260,285)(261,286)(262,287)
(263,288)(264,289)(265,290)(266,291)(267,292)(268,293)(269,294)(270,295)
(271,296)(272,297)(273,298)(274,299)(275,300);
s1 := Sym(300)!( 1, 26)( 2, 30)( 3, 29)( 4, 28)( 5, 27)( 6, 50)( 7, 49)
( 8, 48)( 9, 47)( 10, 46)( 11, 45)( 12, 44)( 13, 43)( 14, 42)( 15, 41)
( 16, 40)( 17, 39)( 18, 38)( 19, 37)( 20, 36)( 21, 35)( 22, 34)( 23, 33)
( 24, 32)( 25, 31)( 52, 55)( 53, 54)( 56, 75)( 57, 74)( 58, 73)( 59, 72)
( 60, 71)( 61, 70)( 62, 69)( 63, 68)( 64, 67)( 65, 66)( 76,101)( 77,105)
( 78,104)( 79,103)( 80,102)( 81,125)( 82,124)( 83,123)( 84,122)( 85,121)
( 86,120)( 87,119)( 88,118)( 89,117)( 90,116)( 91,115)( 92,114)( 93,113)
( 94,112)( 95,111)( 96,110)( 97,109)( 98,108)( 99,107)(100,106)(127,130)
(128,129)(131,150)(132,149)(133,148)(134,147)(135,146)(136,145)(137,144)
(138,143)(139,142)(140,141)(151,251)(152,255)(153,254)(154,253)(155,252)
(156,275)(157,274)(158,273)(159,272)(160,271)(161,270)(162,269)(163,268)
(164,267)(165,266)(166,265)(167,264)(168,263)(169,262)(170,261)(171,260)
(172,259)(173,258)(174,257)(175,256)(176,226)(177,230)(178,229)(179,228)
(180,227)(181,250)(182,249)(183,248)(184,247)(185,246)(186,245)(187,244)
(188,243)(189,242)(190,241)(191,240)(192,239)(193,238)(194,237)(195,236)
(196,235)(197,234)(198,233)(199,232)(200,231)(201,276)(202,280)(203,279)
(204,278)(205,277)(206,300)(207,299)(208,298)(209,297)(210,296)(211,295)
(212,294)(213,293)(214,292)(215,291)(216,290)(217,289)(218,288)(219,287)
(220,286)(221,285)(222,284)(223,283)(224,282)(225,281);
s2 := Sym(300)!( 1,156)( 2,160)( 3,159)( 4,158)( 5,157)( 6,151)( 7,155)
( 8,154)( 9,153)( 10,152)( 11,175)( 12,174)( 13,173)( 14,172)( 15,171)
( 16,170)( 17,169)( 18,168)( 19,167)( 20,166)( 21,165)( 22,164)( 23,163)
( 24,162)( 25,161)( 26,181)( 27,185)( 28,184)( 29,183)( 30,182)( 31,176)
( 32,180)( 33,179)( 34,178)( 35,177)( 36,200)( 37,199)( 38,198)( 39,197)
( 40,196)( 41,195)( 42,194)( 43,193)( 44,192)( 45,191)( 46,190)( 47,189)
( 48,188)( 49,187)( 50,186)( 51,206)( 52,210)( 53,209)( 54,208)( 55,207)
( 56,201)( 57,205)( 58,204)( 59,203)( 60,202)( 61,225)( 62,224)( 63,223)
( 64,222)( 65,221)( 66,220)( 67,219)( 68,218)( 69,217)( 70,216)( 71,215)
( 72,214)( 73,213)( 74,212)( 75,211)( 76,231)( 77,235)( 78,234)( 79,233)
( 80,232)( 81,226)( 82,230)( 83,229)( 84,228)( 85,227)( 86,250)( 87,249)
( 88,248)( 89,247)( 90,246)( 91,245)( 92,244)( 93,243)( 94,242)( 95,241)
( 96,240)( 97,239)( 98,238)( 99,237)(100,236)(101,256)(102,260)(103,259)
(104,258)(105,257)(106,251)(107,255)(108,254)(109,253)(110,252)(111,275)
(112,274)(113,273)(114,272)(115,271)(116,270)(117,269)(118,268)(119,267)
(120,266)(121,265)(122,264)(123,263)(124,262)(125,261)(126,281)(127,285)
(128,284)(129,283)(130,282)(131,276)(132,280)(133,279)(134,278)(135,277)
(136,300)(137,299)(138,298)(139,297)(140,296)(141,295)(142,294)(143,293)
(144,292)(145,291)(146,290)(147,289)(148,288)(149,287)(150,286);
poly := sub<Sym(300)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope