Part of the Atlas of Small Regular Polytopes

Polytope of Type {8,12}

Atlas Canonical Name {8,12}*1152b

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Overview

Group
SmallGroup(1152,32552)
Rank
3
Schläfli Type
{8,12}
Vertices, edges, …
48, 288, 72
Order of s0s1s2
4
Order of s0s1s2s1
12
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

9-fold

16-fold

18-fold

36-fold

72-fold

144-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*s2*s1)^6> of order 2

36 facets

24 vertex figures

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

24 facets

16 vertex figures

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

24 facets

32 vertex figures

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

18 facets

12 vertex figures

P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2> of order 6

12 facets

8 vertex figures

P/N, where N=<(s1*s0*s1*s2)^2> of order 6

12 facets

8 vertex figures

P/N, where N=<s0*(s1*s2)^3*s1*s0*s2, s0*s1*s2*s1*s0*(s1*s2)^5*s1> of order 6

12 facets

16 vertex figures

Representations

Permutation Representation (GAP) 
s0 := (  1, 73)(  2, 74)(  3, 75)(  4, 81)(  5, 79)(  6, 80)(  7, 77)(  8, 78)(  9, 76)( 10, 82)( 11, 83)( 12, 84)( 13, 90)( 14, 88)( 15, 89)( 16, 86)( 17, 87)( 18, 85)( 19, 91)( 20, 92)( 21, 93)( 22, 99)( 23, 97)( 24, 98)( 25, 95)( 26, 96)( 27, 94)( 28,100)( 29,101)( 30,102)( 31,108)( 32,106)( 33,107)( 34,104)( 35,105)( 36,103)( 37,136)( 38,137)( 39,138)( 40,144)( 41,142)( 42,143)( 43,140)( 44,141)( 45,139)( 46,127)( 47,128)( 48,129)( 49,135)( 50,133)( 51,134)( 52,131)( 53,132)( 54,130)( 55,118)( 56,119)( 57,120)( 58,126)( 59,124)( 60,125)( 61,122)( 62,123)( 63,121)( 64,109)( 65,110)( 66,111)( 67,117)( 68,115)( 69,116)( 70,113)( 71,114)( 72,112);;
s1 := (  2,  6)(  3,  8)(  5,  9)( 11, 15)( 12, 17)( 14, 18)( 19, 28)( 20, 33)( 21, 35)( 22, 31)( 23, 36)( 24, 29)( 25, 34)( 26, 30)( 27, 32)( 38, 42)( 39, 44)( 41, 45)( 47, 51)( 48, 53)( 50, 54)( 55, 64)( 56, 69)( 57, 71)( 58, 67)( 59, 72)( 60, 65)( 61, 70)( 62, 66)( 63, 68)( 73,109)( 74,114)( 75,116)( 76,112)( 77,117)( 78,110)( 79,115)( 80,111)( 81,113)( 82,118)( 83,123)( 84,125)( 85,121)( 86,126)( 87,119)( 88,124)( 89,120)( 90,122)( 91,136)( 92,141)( 93,143)( 94,139)( 95,144)( 96,137)( 97,142)( 98,138)( 99,140)(100,127)(101,132)(102,134)(103,130)(104,135)(105,128)(106,133)(107,129)(108,131);;
s2 := (  1,  2)(  4,  8)(  5,  7)(  6,  9)( 10, 11)( 13, 17)( 14, 16)( 15, 18)( 19, 20)( 22, 26)( 23, 25)( 24, 27)( 28, 29)( 31, 35)( 32, 34)( 33, 36)( 37, 65)( 38, 64)( 39, 66)( 40, 71)( 41, 70)( 42, 72)( 43, 68)( 44, 67)( 45, 69)( 46, 56)( 47, 55)( 48, 57)( 49, 62)( 50, 61)( 51, 63)( 52, 59)( 53, 58)( 54, 60)( 73, 74)( 76, 80)( 77, 79)( 78, 81)( 82, 83)( 85, 89)( 86, 88)( 87, 90)( 91, 92)( 94, 98)( 95, 97)( 96, 99)(100,101)(103,107)(104,106)(105,108)(109,137)(110,136)(111,138)(112,143)(113,142)(114,144)(115,140)(116,139)(117,141)(118,128)(119,127)(120,129)(121,134)(122,133)(123,135)(124,131)(125,130)(126,132);;
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, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
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*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(144)!(  1, 73)(  2, 74)(  3, 75)(  4, 81)(  5, 79)(  6, 80)(  7, 77)(  8, 78)(  9, 76)( 10, 82)( 11, 83)( 12, 84)( 13, 90)( 14, 88)( 15, 89)( 16, 86)( 17, 87)( 18, 85)( 19, 91)( 20, 92)( 21, 93)( 22, 99)( 23, 97)( 24, 98)( 25, 95)( 26, 96)( 27, 94)( 28,100)( 29,101)( 30,102)( 31,108)( 32,106)( 33,107)( 34,104)( 35,105)( 36,103)( 37,136)( 38,137)( 39,138)( 40,144)( 41,142)( 42,143)( 43,140)( 44,141)( 45,139)( 46,127)( 47,128)( 48,129)( 49,135)( 50,133)( 51,134)( 52,131)( 53,132)( 54,130)( 55,118)( 56,119)( 57,120)( 58,126)( 59,124)( 60,125)( 61,122)( 62,123)( 63,121)( 64,109)( 65,110)( 66,111)( 67,117)( 68,115)( 69,116)( 70,113)( 71,114)( 72,112);
s1 := Sym(144)!(  2,  6)(  3,  8)(  5,  9)( 11, 15)( 12, 17)( 14, 18)( 19, 28)( 20, 33)( 21, 35)( 22, 31)( 23, 36)( 24, 29)( 25, 34)( 26, 30)( 27, 32)( 38, 42)( 39, 44)( 41, 45)( 47, 51)( 48, 53)( 50, 54)( 55, 64)( 56, 69)( 57, 71)( 58, 67)( 59, 72)( 60, 65)( 61, 70)( 62, 66)( 63, 68)( 73,109)( 74,114)( 75,116)( 76,112)( 77,117)( 78,110)( 79,115)( 80,111)( 81,113)( 82,118)( 83,123)( 84,125)( 85,121)( 86,126)( 87,119)( 88,124)( 89,120)( 90,122)( 91,136)( 92,141)( 93,143)( 94,139)( 95,144)( 96,137)( 97,142)( 98,138)( 99,140)(100,127)(101,132)(102,134)(103,130)(104,135)(105,128)(106,133)(107,129)(108,131);
s2 := Sym(144)!(  1,  2)(  4,  8)(  5,  7)(  6,  9)( 10, 11)( 13, 17)( 14, 16)( 15, 18)( 19, 20)( 22, 26)( 23, 25)( 24, 27)( 28, 29)( 31, 35)( 32, 34)( 33, 36)( 37, 65)( 38, 64)( 39, 66)( 40, 71)( 41, 70)( 42, 72)( 43, 68)( 44, 67)( 45, 69)( 46, 56)( 47, 55)( 48, 57)( 49, 62)( 50, 61)( 51, 63)( 52, 59)( 53, 58)( 54, 60)( 73, 74)( 76, 80)( 77, 79)( 78, 81)( 82, 83)( 85, 89)( 86, 88)( 87, 90)( 91, 92)( 94, 98)( 95, 97)( 96, 99)(100,101)(103,107)(104,106)(105,108)(109,137)(110,136)(111,138)(112,143)(113,142)(114,144)(115,140)(116,139)(117,141)(118,128)(119,127)(120,129)(121,134)(122,133)(123,135)(124,131)(125,130)(126,132);
poly := sub<Sym(144)|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, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
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*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.

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