Part of the Atlas of Small Regular Polytopes

Polytope of Type {8,4}

Atlas Canonical Name {8,4}*1600b

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1600,6690)
Rank
3
Schläfli Type
{8,4}
Vertices, edges, …
200, 400, 100
Order of s0s1s2
40
Order of s0s1s2s1
20
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

25-fold

50-fold

100-fold

200-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<s0*s1*s0*(s2*s1*s0*s1)^4*s2*s1> of order 2

50 facets

100 vertex figures

P/N, where N=<s0*s1*s0*(s2*s1*s0*s1)^2*(s2*s1*s0)^2*s2*s1*s2> of order 5

20 facets

40 vertex figures

P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2> of order 5

20 facets

40 vertex figures

P/N, where N=<s0*s1*(s2*s1*s0)^2*s1*s2*s1*s0*s2*s1> of order 5

20 facets

40 vertex figures

P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2, s0*s1*s0*(s2*s1*s0*s1)^4*s2*s1> of order 10

10 facets

20 vertex figures

Representations

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

References

None.

to this polytope.

Twisty Puzzle