This interactive mathlet is an adaptation of the drawing that Leonardo da Vinci made of the dodecahedron (duodecedron planus vacuus) for Luca Pacioli's book 'De Divina Proportione'.
Pacioli wrote about the dodecahedron (Spanish translation):
"El dodecaedro plano sólido o hueco tiene treinta líneas o lados iguales que forman en él sesenta ángulos superficiales, y tiene
veinte ángulos sólidos y doce bases o superficies que lo contienen. Estas son todas pentagonales, de lados y ángulos iguales entre sí,
como se deduce de su forma."
('La divina proporción' de Luca Pacioli, page 95,Spanish translation by Juan Calatrava, Editorial Akal, 4th edition, 2008)
Leonardo da Vinci's drawing of the dodecahedron (duodecedron vacuus) for Luca Pacioli's book 'De divina proportione'. (There is an Spanish version, 'La divina proporción' Editorial Akal. Image used with permission of Editorial Akal).
Leonardo da Vinci's drawing of the dodecahedron (duodecedron solidus) for Luca Pacioli's book 'De divina proportione'. (There is an Spanish version, 'La divina proporción' Editorial Akal. Image used with permission of Editorial Akal).
REFERENCES
Luca Pacioli - La divina proporción - Ediciones Akal, 4th edition, 2004. Spanish edition of 'De divina proportione'. Translation by Juan Calatrava.
Leonardo da Vinci's Geometric Sketches artículo de Frank J. Swetz en MathDl, Loci:Convergence.
Leonardo da Vinci's Polyhedra página de George Hart en su excelente sitio sobre poliedros.
LINKS
|
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 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.
|
|
Leonardo da Vinci:Drawing of an stellated 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).
|
|
Regular dodecahedron
One eighth of a regular dodecahedon of edge 2 has the same volume as a dodecahedron of edge 1.
|
|
Volume of a regular dodecahedron (Flash version)
One eighth of a regular dodecahedon of edge 2 has the same volume as a dodecahedron of edge 1.
|