Leonardo Stella
Bartolome Beacham
This video is an adaptation of the drawing that Leonardo da Vinci made of the stellated octahedron for Luca Pacioli's book 'De Divina Proportione'.Pacioli named it 'octocedron elevatus vacuus'. A hundred years later, Kepler named this polyhedron 'stella octangula'.
REFERENCESLuca Pacioli - La divina proporcin - Ediciones Akal, 4th edition, 2004. Spanish edition of 'De divina proportione'. Translation by Juan Calatrava.Leonardo da Vinci's Geometric Sketches Frank J. Swetz's article in MathDl, Loci:Convergence.Leonardo da Vinci's Polyhedra George Hart's excellent website about polyhedra.
NEXT Leonardo da Vinci: Drawing of a truncated tetrahedron 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 truncated tetrahedron.
PREVIOUS Leonardo da Vinci: Drawing of a cuboctahedron 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 cuboctahedron.
MORE LINKS Leonardo da Vinci: Drawing of a dodecahedron 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 dodecahedron. Leonardo da Vinci: Drawing of a truncated octahedron 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 truncated octahedron. Leonardo da Vinci:Drawing of a rhombicuboctahedron 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 rhombicuboctahedron. 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. Leonardo da Vinci:Drawing of an octahedron 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 octahedron. Leonardo da Vinci:Drawing of a SEPTUAGINTA 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 Campanus' sphere. Stellated cuboctahedronThe 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. A truncated octahedron made by eight half cubesUsing eight half cubes we can make a truncated octahedron. The cube tesselate the space an so do the truncated octahedron. We can calculate the volume of a truncated octahedron. Volume of a regular dodecahedronOne eighth of a regular dodecahedon of edge 2 has the same volume as a dodecahedron of edge 1. The volume of the tetrahedronThe volume of a tetrahedron is one third of the prism that contains it. Plane developments of geometric bodies: TetrahedronThe first drawing of a plane net of a regular tetrahedron was published by Drer in his book 'Underweysung der Messung' ('Four Books of Measurement'), published in 1525 . Volume of an octahedronThe 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. The volume of a truncated octahedronThe 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 a cuboctahedronA 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. The truncated octahedron is a space-filling polyhedronThese polyhedra pack together to fill space, forming a 3 dimensional space tessellation or tilling. Truncated tetrahedronThe truncated tetrahedron is an Archimedean solid made by 4 triangles and 4 hexagons. Truncations of the cube and octahedronWhen you truncate a cube you get a truncated cube and a cuboctahedron. If you truncate an octahedron you get a truncated octahedron and a cuboctahedron.
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