Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,24}

Atlas Canonical Name {4,24}*768l

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(768,1087808)
Rank
3
Schläfli Type
{4,24}
Vertices, edges, …
16, 192, 96
Order of s0s1s2
12
Order of s0s1s2s1
8
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

16-fold

24-fold

32-fold

48-fold

64-fold

96-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*(s2*s1)^4*s2> of order 2

48 facets

8 vertex figures

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

48 facets

8 vertex figures

P/N, where N=<(s0*(s2*s1)^3)^2> of order 2

48 facets

8 vertex figures

P/N, where N=<s0*s1*s0*(s2*s1)^2*s0*s2*s1*s0*s2> of order 3

32 facets

8 vertex figures

P/N, where N=<(s0*(s2*s1)^3)^2, (s0*s1)^2*s2*s1*s0*(s1*s2)^4> of order 4

24 facets

4 vertex figures

P/N, where N=<(s0*s2*s1)^3> of order 4

24 facets

4 vertex figures

Representations

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

References

None.

to this polytope.

Twisty Puzzle