Tetradecahedron

A tetradecahedron is a polyhedron with 14 faces. There are numerous topologically distinct forms of a tetradecahedron, with many constructible entirely with regular polygon faces.

A tetradecahedron is sometimes called a tetrakaidecahedron.[1][2] No difference in meaning is ascribed.[3][4]. The interposition of "kai" probably is due to its meaning in Greek language as a Grammatical conjunction (meaning the same as "and" in the English language).

An incomplete list of forms includes:

• Tetradecahedra having all regular polygonal faces (all exist in irregular-faced forms as well):
  • Archimedean solids:
    • Cuboctahedron (8 equilateral triangles, 6 squares)
    • Truncated cube (8 equilateral triangles, 6 octagons)
    • Truncated octahedron (6 squares, 8 regular hexagons)
  • Prisms and antiprisms:
    • Dodecagonal prism (12 squares, 2 regular dodecagons)
    • Hexagonal antiprism (12 equilateral triangles, 2 regular hexagons)
  • Johnson solids:
    • J₁₈: Elongated triangular cupola (4 equilateral triangles, 9 squares, 1 regular hexagon)
    • J₂₇: Triangular orthobicupola (8 equilateral triangles, 6 squares)
    • J₅₁: Triaugmented triangular prism (14 equilateral triangles)
    • J₅₅: Parabiaugmented hexagonal prism (8 equilateral triangles, 4 squares, 2 regular hexagons)
    • J₅₆: Metabiaugmented hexagonal prism (8 equilateral triangles, 4 squares, 2 regular hexagons)
    • J₆₅: Augmented truncated tetrahedron (8 equilateral triangles, 3 squares, 3 regular hexagons)
    • J₈₆: Sphenocorona (12 equilateral triangles, 2 squares)
    • J₉₁: Bilunabirotunda (8 equilateral triangles, 2 squares, 4 regular pentagons)

• Tetradecahedra having at least one irregular face:
  • Heptagonal dipyramid (14 triangles) (see Dipyramid)
  • Heptagonal trapezohedron (14 kites) (see Trapezohedron)
  • Tridecagonal pyramid (13 triangles, 1 regular tridecagon) (see Pyramid (geometry))
  • Dissected regular icosahedron (the vertex figure of the grand antiprism) (12 equilateral triangles and 2 trapezoids)
  • Hexagonal truncated trapezohedron: (12 pentagons, 2 hexagons)
    Includes an optimal space-filling shape in foams (see Weaire-Phelan structure) and in the crystal structure of Clathrate hydrate (see illustration, next to label 5¹²6²)

See also

• Császár polyhedron - A nonconvex tetradecahedron of all triangle faces
• Permutohedron

External links

• Weisstein, Eric W., "Tetradecahedron" from MathWorld.