Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,100}

Atlas Canonical Name {6,100}*1800

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Overview

Group
SmallGroup(1800,226)
Rank
3
Schläfli Type
{6,100}
Vertices, edges, …
9, 450, 150
Order of s0s1s2
100
Order of s0s1s2s1
6
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Non-Orientable

Quotients maximal quotients in bold

5-fold

25-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

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)( 76,151)( 77,152)( 78,153)( 79,154)( 80,155)( 81,156)( 82,157)( 83,158)( 84,159)( 85,160)( 86,161)( 87,162)( 88,163)( 89,164)( 90,165)( 91,166)( 92,167)( 93,168)( 94,169)( 95,170)( 96,171)( 97,172)( 98,173)( 99,174)(100,175)(101,201)(102,202)(103,203)(104,204)(105,205)(106,206)(107,207)(108,208)(109,209)(110,210)(111,211)(112,212)(113,213)(114,214)(115,215)(116,216)(117,217)(118,218)(119,219)(120,220)(121,221)(122,222)(123,223)(124,224)(125,225)(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);;
s1 := (  1, 76)(  2, 80)(  3, 79)(  4, 78)(  5, 77)(  6, 97)(  7, 96)(  8,100)(  9, 99)( 10, 98)( 11, 92)( 12, 91)( 13, 95)( 14, 94)( 15, 93)( 16, 87)( 17, 86)( 18, 90)( 19, 89)( 20, 88)( 21, 82)( 22, 81)( 23, 85)( 24, 84)( 25, 83)( 26,101)( 27,105)( 28,104)( 29,103)( 30,102)( 31,122)( 32,121)( 33,125)( 34,124)( 35,123)( 36,117)( 37,116)( 38,120)( 39,119)( 40,118)( 41,112)( 42,111)( 43,115)( 44,114)( 45,113)( 46,107)( 47,106)( 48,110)( 49,109)( 50,108)( 51,126)( 52,130)( 53,129)( 54,128)( 55,127)( 56,147)( 57,146)( 58,150)( 59,149)( 60,148)( 61,142)( 62,141)( 63,145)( 64,144)( 65,143)( 66,137)( 67,136)( 68,140)( 69,139)( 70,138)( 71,132)( 72,131)( 73,135)( 74,134)( 75,133)(152,155)(153,154)(156,172)(157,171)(158,175)(159,174)(160,173)(161,167)(162,166)(163,170)(164,169)(165,168)(177,180)(178,179)(181,197)(182,196)(183,200)(184,199)(185,198)(186,192)(187,191)(188,195)(189,194)(190,193)(202,205)(203,204)(206,222)(207,221)(208,225)(209,224)(210,223)(211,217)(212,216)(213,220)(214,219)(215,218);;
s2 := (  1,  6)(  2, 10)(  3,  9)(  4,  8)(  5,  7)( 11, 22)( 12, 21)( 13, 25)( 14, 24)( 15, 23)( 16, 17)( 18, 20)( 26, 81)( 27, 85)( 28, 84)( 29, 83)( 30, 82)( 31, 76)( 32, 80)( 33, 79)( 34, 78)( 35, 77)( 36, 97)( 37, 96)( 38,100)( 39, 99)( 40, 98)( 41, 92)( 42, 91)( 43, 95)( 44, 94)( 45, 93)( 46, 87)( 47, 86)( 48, 90)( 49, 89)( 50, 88)( 51,156)( 52,160)( 53,159)( 54,158)( 55,157)( 56,151)( 57,155)( 58,154)( 59,153)( 60,152)( 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)(101,106)(102,110)(103,109)(104,108)(105,107)(111,122)(112,121)(113,125)(114,124)(115,123)(116,117)(118,120)(126,181)(127,185)(128,184)(129,183)(130,182)(131,176)(132,180)(133,179)(134,178)(135,177)(136,197)(137,196)(138,200)(139,199)(140,198)(141,192)(142,191)(143,195)(144,194)(145,193)(146,187)(147,186)(148,190)(149,189)(150,188)(201,206)(202,210)(203,209)(204,208)(205,207)(211,222)(212,221)(213,225)(214,224)(215,223)(216,217)(218,220);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*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(225)!( 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)( 76,151)( 77,152)( 78,153)( 79,154)( 80,155)( 81,156)( 82,157)( 83,158)( 84,159)( 85,160)( 86,161)( 87,162)( 88,163)( 89,164)( 90,165)( 91,166)( 92,167)( 93,168)( 94,169)( 95,170)( 96,171)( 97,172)( 98,173)( 99,174)(100,175)(101,201)(102,202)(103,203)(104,204)(105,205)(106,206)(107,207)(108,208)(109,209)(110,210)(111,211)(112,212)(113,213)(114,214)(115,215)(116,216)(117,217)(118,218)(119,219)(120,220)(121,221)(122,222)(123,223)(124,224)(125,225)(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);
s1 := Sym(225)!(  1, 76)(  2, 80)(  3, 79)(  4, 78)(  5, 77)(  6, 97)(  7, 96)(  8,100)(  9, 99)( 10, 98)( 11, 92)( 12, 91)( 13, 95)( 14, 94)( 15, 93)( 16, 87)( 17, 86)( 18, 90)( 19, 89)( 20, 88)( 21, 82)( 22, 81)( 23, 85)( 24, 84)( 25, 83)( 26,101)( 27,105)( 28,104)( 29,103)( 30,102)( 31,122)( 32,121)( 33,125)( 34,124)( 35,123)( 36,117)( 37,116)( 38,120)( 39,119)( 40,118)( 41,112)( 42,111)( 43,115)( 44,114)( 45,113)( 46,107)( 47,106)( 48,110)( 49,109)( 50,108)( 51,126)( 52,130)( 53,129)( 54,128)( 55,127)( 56,147)( 57,146)( 58,150)( 59,149)( 60,148)( 61,142)( 62,141)( 63,145)( 64,144)( 65,143)( 66,137)( 67,136)( 68,140)( 69,139)( 70,138)( 71,132)( 72,131)( 73,135)( 74,134)( 75,133)(152,155)(153,154)(156,172)(157,171)(158,175)(159,174)(160,173)(161,167)(162,166)(163,170)(164,169)(165,168)(177,180)(178,179)(181,197)(182,196)(183,200)(184,199)(185,198)(186,192)(187,191)(188,195)(189,194)(190,193)(202,205)(203,204)(206,222)(207,221)(208,225)(209,224)(210,223)(211,217)(212,216)(213,220)(214,219)(215,218);
s2 := Sym(225)!(  1,  6)(  2, 10)(  3,  9)(  4,  8)(  5,  7)( 11, 22)( 12, 21)( 13, 25)( 14, 24)( 15, 23)( 16, 17)( 18, 20)( 26, 81)( 27, 85)( 28, 84)( 29, 83)( 30, 82)( 31, 76)( 32, 80)( 33, 79)( 34, 78)( 35, 77)( 36, 97)( 37, 96)( 38,100)( 39, 99)( 40, 98)( 41, 92)( 42, 91)( 43, 95)( 44, 94)( 45, 93)( 46, 87)( 47, 86)( 48, 90)( 49, 89)( 50, 88)( 51,156)( 52,160)( 53,159)( 54,158)( 55,157)( 56,151)( 57,155)( 58,154)( 59,153)( 60,152)( 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)(101,106)(102,110)(103,109)(104,108)(105,107)(111,122)(112,121)(113,125)(114,124)(115,123)(116,117)(118,120)(126,181)(127,185)(128,184)(129,183)(130,182)(131,176)(132,180)(133,179)(134,178)(135,177)(136,197)(137,196)(138,200)(139,199)(140,198)(141,192)(142,191)(143,195)(144,194)(145,193)(146,187)(147,186)(148,190)(149,189)(150,188)(201,206)(202,210)(203,209)(204,208)(205,207)(211,222)(212,221)(213,225)(214,224)(215,223)(216,217)(218,220);
poly := sub<Sym(225)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*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.

Twisty Puzzle