Augmented Rhombicuboctahedron II (adapted from Leonardo)
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This is a second interactive versión of Leonardo da Vinci's drawing of the augmented rhombicuboctahedron.
Leonardo da Vinci made several drawings of polyhedra for Luca Pacioli's book 'De divina proportione'. Here we can see an adaptation of the augmented rhombicuboctahedron.
In this version we can see the interior of this polyhedron. Luca Pacioli wrote that 'you can only see the interior using your imagination'.
We can separate the pyramids and see that the interior is a rhombicuboctahedron.
Leonardo da Vinci made several drawings of polyhedra for Luca Pacioli's book 'De divina proportione'. Here we can see an adaptation of the rhombicuboctahedron.
You can play with an augmented rhombicuboctahedron with different pyramids sizes clicking the next link:
Starting with a Rhombicubotahedron we can add pyramids over each face. The we get a beautiful polyhedron that it is like a star.
REFERENCES
Luca Pacioli - La divina proporción - Ediciones Akal, 4th edition, 2004. Spanish edition of 'De divina proportione'. Translation by Juan Calatrava.
Rinus Roelofs' web site. Sculptor and Mathematician Rinus Roelofs has a wonderful web site full of
beautiful ideas and resources. One example, his article A Mistake in a drawing by Leonardo da Vinci.
W.W.W. Rouse Ball and H.S.M. Coxeter, 'Mathematical Recreatins & Essays', The Macmillan Company, New York, 1947.
Pseudo Rhombicuboctahedra in George Hart's excellent website about polyhedra.
Peter R. Cromwell - 'Polyhedra', Cambridge University Press, 1999. (pp. 89 and 366-369)
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Starting with a Rhombicubotahedron we can add pyramids over each face. The we get a beautiful polyhedron that it is like a star.
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Leonardo da Vinci made several drawings of polyhedra for Luca Pacioli's book 'De divina proportione'. Here we can see an adaptation of the augmented rhombicuboctahedron.
MORE LINKS
Leonardo da Vinci made several drawings of polyhedra for Luca Pacioli's book 'De divina proportione'. Here we can see an adaptation of the rhombicuboctahedron.
This polyhedron is also called Elongated Square Gyrobicupola. It is similar to the Rhombicuboctahedron but it is less symmetric.
Adding six pyramids to a cube you can build new polyhedra with twenty four triangular faces. For specific pyramids you get a Rhombic Dodecahedron that has twelve rhombic faces.
Leonardo da Vinci made several drawings of polyhedra for Luca Pacioli's book 'De divina proportione'. Here we can see an adaptation of the dodecahedron.
Leonardo da Vinci made several drawings of polyhedra for Luca Pacioli's book 'De divina proportione'. Here we can see an adaptation of the truncated octahedron.
Leonardo da Vinci made several drawings of polyhedra for Luca Pacioli's book 'De divina proportione'. Here we can see an adaptation of the cuboctahedron.
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).
Leonardo da Vinci made several drawings of polyhedra for Luca Pacioli's book 'De divina proportione'. Here we can see an adaptation of the octahedron.
Leonardo da Vinci made several drawings of polyhedra for Luca Pacioli's book 'De divina proportione'. Here we can see an adaptation of the truncated tetrahedron.
Leonardo da Vinci made several drawings of polyhedra for Luca Pacioli's book 'De divina proportione'. Here we can see an adaptation of the Campanus' sphere.
Adding six pyramids to a cube you can build new polyhedra with twenty four triangular faces. For specific pyramids you get a Rhombic Dodecahedron that has twelve rhombic faces.
You can build a Rhombic Dodecahedron adding six pyramids to a cube. This fact has several interesting consequences.
The first drawing of a plane net of a regular octahedron was published by Dürer in his book 'Underweysung der Messung' ('Four Books of Measurement'), published in 1525 .
Using cardboard you can build beautiful polyhedra cutting polygons and glue them toghether. This is a very simple and effective technique. You can download several templates. Then print, cut and glue: very easy!
A very simple technique to build complex and colorful polyhedra.
Material for a session about polyhedra (Zaragoza, 7th November 2014). We study the octahedron and the tetrahedron and their volumes. The truncated octahedron helps us to this task. We build a cubic box with cardboard and an origami tetrahedron.
Material for a session about polyhedra (Zaragoza, 23rd Octuber 2015) . Building a cube with cardboard and an origami octahedron.
Material for a session about polyhedra (Zaragoza, 13th Abril 2012).
Material for a session about polyhedra (Zaragoza, 9th May 2014). Simple techniques to build polyhedra like the tetrahedron, octahedron, the cuboctahedron and the rhombic dodecahedron. We can build a box that is a rhombic dodecahedron.
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.