Truncated triangular trapezohedron

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Truncated triangular trapezohedron
Dürer's solid
Triangular truncated trapezohedron.png
Type Truncated trapezohedron
Faces6 pentagons,
2 triangles
Symmetry group D3d, [2+,6], (2*3)
Dual polyhedron Gyroelongated triangular bipyramid

In geometry, the truncated triangular trapezohedron is the first in an infinite series of truncated trapezohedron polyhedra. It has 6 pentagon and 2 triangle faces.



This polyhedron can be constructed by truncating two opposite vertices of a cube, of a trigonal trapezohedron (a convex polyhedron with six congruent rhombus sides, formed by stretching or shrinking a cube along one of its long diagonals), or of a rhombohedron or parallelepiped (less symmetric polyhedra that still have the same combinatorial structure as a cube). In the case of a cube, or of a trigonal trapezohedron where the two truncated vertices are the ones on the stretching axes, the resulting shape has three-fold rotational symmetry.

Dürer's solid

Melencolia I. Durer Melancholia I.jpg
Melencolia I .

This polyhedron is sometimes called Dürer's solid, from its appearance in Albrecht Dürer's 1514 engraving Melencolia I . The graph formed by its edges and vertices is called the Dürer graph.

The shape of the solid depicted by Dürer is a subject of some academic debate. [1] According to Lynch (1982), the hypothesis that the shape is a misdrawn truncated cube was promoted by Strauss (1972); however most sources agree that it is the truncation of a rhombohedron. Despite this agreement, the exact geometry of this rhombohedron is the subject of several contradictory theories:

See also


  1. See Weitzel (2004) and Ziegler (2014), from which much of the following history is drawn.

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<i>Melencolia I</i> 1514 engraving by Albrecht Dürer

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