Tetracube-Pentacube Pair Oddities


A tetracube is a solid made of 4 equal cubes joined face to face. There are 8 tetracubes, counting distinct mirror images.

A pentacube is a solid made of 5 equal cubes joined face to face. There are 29 pentacubes, counting distinct mirror images.

A polyform oddity or Sillke Figure is a polyform with binary symmetry at least, tiled by an odd number of copies of a given polyform.

Here I show polycubes with full symmetry and an odd number of cells, formed by joining copies of a given tetracube and a given pentacube. The solutions are the smallest known to me. The figures shown are the numbers of tiles used.

If you find a smaller solution, please write.

See also Pentacube Pair Oddities.

Table of Results


25 Cells

27 Cells

49 Cells

57 Cells

61 Cells

63 Cells

67 Cells

73 Cells

75 Cells

79 Cells

81 Cells

87 Cells

93 Cells

99 Cells

105 Cells

109 Cells

111 Cells

113 Cells

117 Cells

119 Cells

123 Cells

125 Cells

129 Cells

147 Cells

213 Cells

225 Cells

267 Cells


Last revised 2023-02-10.

Back to Polyform Oddities < Polyform Curiosities
Col. George Sicherman [ HOME | MAIL ]