Truncated triangular trapezohedron
In geometry, the truncated triangular trapezohedron is the first in an infinite series of truncated trapezohedra. It has 6 pentagon and 2 triangle faces.
Melencolia I.
Melencolia I is a large 1514 engraving by the German Renaissance artist Albrecht Dürer. Its central subject is an enigmatic and gloomy winged female figure thought to be a personification of melancholia – melancholy. Holding her head in her hand, she stares past the busy scene in front of her. The area is strewn with symbols and tools associated with craft and carpentry, including an hourglass, weighing scales, a hand plane, a claw hammer, and a saw. Other objects relate to alchemy, geometry or numerology. Behind the figure is a structure with an embedded magic square, and a ladder leading beyond the frame. The sky contains a rainbow, a comet or planet, and a bat-like creature bearing the text that has become the print's title.
Melencolia I (with annotations)
Dürer's Virgin and Child Seated by a Wall (1514) is compositionally similar to Melencolia I in the position of the figures and structures, but is much more coherent to the eye. This comparison highlights the disturbing function of the polyhedron in Melencolia I.
A 4×4 magic square has columns, rows, and diagonals that sum to 34. In this configuration, many other sets of four squares also sum to 34. Dürer includes the year in the two bottom squares, and the squares adding to 5 and 17 may refer to his mother's death in May of that year. (First number of second row is "5" and third row "9").
An earlier woodcut with an allegory of geometry from Gregor Reisch's Margarita philosophica. It depicts many objects also seen in Melencolia I.
