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This interactive mathlet is an adaptation of the drawing that Leonardo da Vinci made of the cuboctahedron exacedron abscisus vacuus for Luca Pacioli’s book ‘De Divina Proportione’. Spanish edition of ‘De divina proportione’. Translation by Juan Calatrava. luac

### La divina proporción. Luca Pacioli | Old Science | Pinterest | Luca pacioli and Science

Swetz’s article in MathDl, Loci: Leonardo da Vinci’s Polyhedra George Hart’s excellent website about polyhedra. Drawing of an pxcioli octahedron stella octangula made to Luca Pacioli’s De divina proportione.

Leonardo da Vinci made several drawings of polyhedra for Luca Pacioli’s book ‘De divina proportione’. Here we can see an adaptation of the stellated octahedron stella octangula. Drawing of a truncated octahedron made to Luca Pacioli’s De divina proportione.

Here we can see an adaptation of the truncated octahedron. Drawing of a dodecahedron made to Luca Pacioli’s De divina proportione. Here we can see an adaptation of the dodecahedron.

Drawing of a truncated tetrahedron made to Luca Pacioli’s De divina proportione. Here we can see an adaptation of the truncated tetrahedron. Drawing of an octahedron made to Luca Pacioli’s De divina proportione. Here we can see an adaptation of the octahedron. Drawing of a rhombicuboctahedron made to Luca Pacioli’s De divina proportione.

Here we can see an adaptation of the rhombicuboctahedron. Here we can see an adaptation of the Campanus’ sphere. The volume of a cuboctahedron A cuboctahedron is an Archimedean solid. It can be seen as made by cutting off the corners of a cube. The volume of a cuboctahedron II A cuboctahedron is an Archimedean solid. It can be seen as made by cutting off the corners of an octahedron. Stellated cuboctahedron The compound polyhedron of a cube and an octahedron is an stellated cuboctahedron.

It is the same to say that the cuboctahedron is the solid common to the cube and the octahedron in this polyhedron. Volume of a regular dodecahedron One eighth of a regular dodecahedon of edge 2 has the same volume as a dodecahedron of edge 1.

The volume of the tetrahedron The volume of a tetrahedron is one third of the prism that contains it. Volume of an octahedron The volume of an octahedron is four times the volume of a tetrahedron.

It is easy to calculate and then we can get the volume of a tetrahedron. Plane developments of geometric bodies: The volume of a truncated octahedron The truncated octahedron is an Archimedean solid. It has 8 regular hexagonal faces and 6 square faces. Its volume can be calculated knowing the volume of an octahedron. The volume of an stellated octahedron stella octangula The stellated octahedron was drawn by Leonardo for Luca Pacioli’s book ‘De Divina Proportione’.

A hundred years later, Kepler named it stella octangula. The truncated octahedron is a space-filling polyhedron These polyhedra pack together to fill space, forming a 3 dimensional space tessellation or tilling. Truncated tetrahedron The truncated tetrahedron is an Archimedean solid made by 4 triangles and 4 hexagons.

Truncations of the cube and octahedron When you truncate a cube you get a truncated cube and a cuboctahedron.

### – La divina proporcion by Luca Pacioli

If you truncate an octahedron you get a truncated octahedron and a cuboctahedron. Chamfered Cube You can chamfer a cube and then you get a polyhedron similar but not equal to a truncated octahedron.

You can get also a rhombic dodecahedron. Pacioli wrote about the cuboctahedron Spanish translation: Y este cuerpo se origina del cubo mediante el corte uniforme en la mitad de sus lados, como demuestra de modo evidente su propia forma material. Leonardo da Vinci’s drawing of the cuboctahedron exacedron abscisus vacuus for Luca Pacioli’s book ‘De divina proportione’.

Image used with permission of Editorial Akal.

## 9788476007877 – La divina proporcion by Luca Pacioli

priporcion Leonardo da Vinci’s drawing of the cuboctahedron exacedron abscisus solidus for Luca Pacioli’s book ‘De divina proportione’. The volume of a cuboctahedron. A cuboctahedron is an Archimedean solid. The volume of a cuboctahedron II. The compound polyhedron of a cube and an octahedron is an stellated cuboctahedron.

Volume of a regular dodecahedron. One eighth of a regular dodecahedon of edge 2 has the same volume as a dodecahedron of edge 1. The volume of the tetrahedron. The volume of a tetrahedron is one third paciili the prism that contains it.

Volume of an octahedron. The volume of an octahedron is four times the volume of a tetrahedron. The volume of a truncated octahedron. The truncated octahedron is an Archimedean solid. The volume of an stellated octahedron stella octangula. The truncated octahedron is a space-filling polyhedron.

These polyhedra pack together to fill space, forming a 3 dimensional space propogcion or tilling. The truncated tetrahedron is an Archimedean solid made by 4 triangles and 4 hexagons. Truncations of the cube and octahedron. When you truncate a cube you get a truncated cube and a cuboctahedron. You can chamfer a cube and then you get a polyhedron similar but not equal to a truncated octahedron.