# 4D Euclidean space

## News Archive

### Jun 2023

This month's Polytope of the Month is the triakis octahedron, another of the Catalan solids:

It is the dual of the truncated cube, and has a surface consisting of 24 equivalent isosceles triangles, each having two short edges and a long edge in the ratio (2−√2) : 1. There are 24 short edges and 12 long edges in the entire polyhedron, and 14 vertices in total.

Find out more on the triakis octahedron page! As usual, we provide full algebraic coordinates for this polyhedron.

**1 Jun 2023:**The Polytope of the Month is up!

### May 2023

This month we return to 3D and continue our series of Catalan solids:

This is the deltoidal icositetrahedron, the dual of the rhombicuboctahedron. It is bounded by 24 kites, 48 edges (12 short, 12 long) with a length ratio of (4+√2) : 7 (approximately 1 : 1.293), and 26 vertices.

For more details, check out the deltoidal icositetrahedron page. As usual, we provide full algebraic coordinates.

**1 May 2023:**The Polytope of the Month is up!

Fixed some incorrect statements in the 4D Catalans page.

### Apr 2023

This month, we introduce our first 4D Catalan polychoron:

This is the joined pentachoron, the dual of the rectified 5-cell. It is bounded by 10 triangular bipyramids, 30 isosceles triangles (with edge length ratio 2 : 2 : 3), 30 edges (10 long, 20 short), and 10 vertices. Its projection envelope is a triakis tetrahedron.

Find out more on the joined pentachoron page! As usual, full Cartesian coordinates are provided.

**1 Apr 2023:**The Polytope of the Month is up, the first of the 4D Catalans!

**10 Apr 2023:**Listed some interesting properties of the Catalan polychora.