The Triakis Octahedron


The triakis octahedron is a 3D Catalan solid bounded by 24 isosceles triangles, 36 edges (24 short, 12 long), and 14 vertices. It is the dual of the truncated cube.

The triakis
octahedron

The faces are transitive; isosceles triangles with two short edges and a long edge with a (2−√2) : 1 length ratio, or approximately 0.586 : 1.

The 14 vertices are of three kinds: 6 axial vertices corresponding to an inscribed octahedron, and 8 vertices corresponding to an inscribed cube.

Projections

The following are images of the triakis octahedron from various viewpoints:

Projection Description

Front view, centered on axial vertex.

Side view, centered on a long edge.

Octant view, centered on a cube vertex.

Animation

Here's an animation of a triakis octahedron rotating around the vertical axis:

Triakis octahedron
rotating

Coordinates

The Cartesian coordinates for the triakis octahedron are all permutations of coordinate and changes of sign of:

These coordinates correspond with a dual truncated cube of edge length (6−4√2).


Last updated 31 May 2023.

Powered by Apache Runs on Debian GNU/Linux Viewable on any browser Valid CSS Valid HTML 5! Proud to be Microsoft-free