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What is an Archimedean Solid? – The following information is from Brittanica Kids with a few definitions added. 

In geometry, the Archimedean solids are a special group of 13 semi-regular polyhedrons. They have a high degree of symmetry. A polyhedron is a geometric solid (three-dimensional shape) whose faces are each flat polygons. A polygon is a plane shape (two-dimensional) with straight sides such as a triangle, square, or octagon. In an Archimedean solid, the faces are regular polygons—that is, their sides are all of equal length. Additionally, an Archimedean solid has faces of two or more different types of regular polygons, such as squares and triangles. The vertices, or corners, of an Archimedean solid are all alike meaning that they are all the same angles. An Archimedean solid can be placed inside a sphere so that every vertex touches the surface of the sphere.

The ancient Greek philosopher Archimedes first described such solids. However, his works on the subject were lost and known only through other writers such as Pappus of Alexandria. Renaissance artists rediscovered several of the Archimedean solids. The Renaissance was a period in European history covering the 15th – 17th centuries (1400-1700). In 1619 the German mathematician and astronomer Johannes Kepler reconstructed the entire set of 13 and gave them Latin names.

Plato, who lived about a century before Archimedes, had described five regular solids in which all the faces are identical regular polyhedrons. These solids, now called the Platonic solids, are the tetrahedron, the cube, the octahedron, the dodecahedron, and the icosahedron. Some of the Archimedean solids can be thought of as variations on the Platonic solids. For example, if one starts with a cube and slices off each corner, leaving an equilateral triangle at each of the eight former corners and a regular octagon (eight-sided figure) in place of the former faces of the cube, the result is a solid with 14 faces: eight triangles and six octagons. Each vertex of the new solid brings together one of the triangles and two of the octagons. This Archimedean solid is called a truncated cube.

If one repeats the procedure but slices off the corners of the cube more deeply, so the triangles meet and only a much smaller square remains on each of the former faces of the cube, the faces of the resulting figure are eight triangles and six squares. Two triangles and two squares meet at each vertex. This is called a cuboctahedron.

Archimedean and Platonic solids are used in various kinds of modern construction such as geodesic domes because their shapes are quite stable. Most soccer balls are spherical variations on a truncated icosahedron, made up of pentagons and hexagons, with one pentagon and two hexagons meeting at each vertex.

The following is a listing of all Archimedean solids from Kiddle

Image Name Faces Type Edges Vertices
Truncated tetrahedron Truncated tetrahedron 8
  • 4 triangles
  • 4 hexagons
18 12
Cubocthahedron Cubocthahedron 14
  • 8 triangles
  • 6 squares
24 12
 Truncated cube Truncated cube 14
  • 8 triangles
  • 6 octagons
36 24
Truncated octahedron Truncated octahedron 14
  • 6 squares
  • 8 hexagons
36 24
Rhombicuboctahedron 26
  • 8 triangles
  • 18 squares
48 24
Truncated cuboctahedron Truncated cuboctahedron 26
  • 12 squares
  • 8 hexagons
  • 6 octagons
72 48
Snub cube

Snub cube

Snub cube (2 mirrored versions) 38
  • 32 triangles
  • 6 squares
60 24
Icosidodecahedron Icosidodecahedron 32
  • 20 triangles
  • 12 pentagons
60 30
Truncated dodecahedron Truncated dodecahedron 32
  • 20 triangles
  • 12 decagons
90 60
Truncated icosahedron Truncated icosahedron 32
  • 12 pentagons
  • 20 hexagons
90 60
Rhombicosidodecahedron Rhombicosidodecahedron 62
  • 20 triangles
  • 30 squares
  • 12 pentagons
120 60
Truncated icosidodecahedron Truncated icosidodecahedron 62
  • 30 squares
  • 20 hexagons
  • 12 decagons
180 120
Snub dodecahedron
Snub dodecahedron
Snub dodecahedron (2 mirrored versions) 92
  • 80 triangles
  • 12 pentagon
150 60

To learn even more about Archimedean Solids join us on November 25th for Advanced STEM Club where we will be making our own paper Archimedean Solids.

Materials:

  • Template printed on cardstock

    If you would like to try a more difficult solid use this template

  • Scissors

  • Glue (a glue stick will work best but any will do)

  • Markers or other coloring materials (optional)