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## La Divina Proporcion

Image used with permission of Editorial Akal. Leonardo da Vinci’s drawing of the dviina octahedron octocedron abscisus vacuus for Luca Pacioli’s book ‘De divina proportione’. Here we can see an adaptation of the stellated octahedron stella octangula. The truncated octahedron is a space-filling polyhedron. Here we can see an adaptation of the dodecahedron. Truncated tetrahedron The truncated tetrahedron is an Archimedean solid made by 4 triangles and 4 hexagons. Plane developments of geometric bodies: Chamfered Cube You can chamfer a cube and then you get a polyhedron similar but not equal to a truncated octahedron.

This interactive mathlet is an adaptation of the drawing that Leonardo da Vinci made of the truncated octahedron octocedron abscisus vacuus for Luca Pacioli’s book ‘De Divina Proportione’.

Truncations of the cube and octahedron When you truncate a cube you get xe truncated cube and a cuboctahedron. It is the same to say that the cuboctahedron is the solid common to the cube and the octahedron in this polyhedron. You can get also a rhombic dodecahedron.

Truncations of the cube and octahedron When you truncate a cube you get a truncated cube and a cuboctahedron. It can be seen as made by cutting off the corners of fe octahedron. Leonardo da Vinci’s Polyhedra George Hart’s excellent website about polyhedra. Drawing of an octahedron made to Luca Pacioli’s De divina proportione. Its volume can be calculated knowing the volume of an octahedron.

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The volume of an octahedron is four times the volume of a tetrahedron. The volume of a tetrahedron is one third of the prism that contains it. It can be seen as made by cutting off the corners of a cube.

A truncated octahedron made by eight half cubes Using eight half cubes we can make a truncated octahedron. A cuboctahedron is an Archimedean solid. Leonardo da Vinci’s drawing of the truncated octahedron octocedron abscisus solidus for Luca Pacioli’s book ‘De divina proportione’. The volume of the tetrahedron The volume of a tetrahedron is one third of the prism that contains it. Here we can see an adaptation of the Campanus’ sphere.

Drawing of a truncated tetrahedron made to Luca Pacioli’s De divina proportione. The volume of a cuboctahedron. It can be seen as made by cutting dee the corners of an octahedron.

Using eight of this pieces we can made a truncated octahedron. It has 8 regular hexagonal faces and 6 square faces. Drawing of a truncated octahedron made to Luca Pacioli’s De divina proportione. Here we can see an adaptation of the octahedron. Stellated cuboctahedron The compound polyhedron of a cube and an octahedron is an stellated cuboctahedron.

Leonardo da Vinci’s drawing of the cuboctahedron exacedron abscisus vacuus for Luca Pacioli’s book ‘De divina proportione’. These polyhedra pack together to fill space, forming a 3 dimensional space tessellation or tilling. Truncations of the cube pacili octahedron. Drawing of a dodecahedron made to Luca Pacioli’s De divina proportione. Pacioli wrote about the truncated octahedron Spanish translation: The volume of a cuboctahedron II A cuboctahedron is an Archimedean solid.