Truncated triangular trapezohedron

Truncated triangular trapezohedron
Dürer's solid
TypeTruncated trapezohedron
Faces6 pentagons,
2 triangles
Edges18
Vertices12
Symmetry groupD3d, [2+,6], (2*3)
Dual polyhedronGyroelongated triangular dipyramid
Propertiesconvex

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.

Geometry

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

Melancolia 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

Notes

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

References

External links


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