# 4D Euclidean space

## News Archive

### Sep 2023

This month, we return to 4D and introduce another Catalan polychoron:

This is the triangular antitegmatic hexacontatetrachoron, the dual of the runcinated tesseract. It is bounded by 64 triangular trapezohedra, 192 kites, 208 edges, and 80 vertices. Its projection envelope is the deltoidal icositetrahedron (in exact proportions), a Catalan solid which is also its direct 3D analogue.

Check out the triangular antitegmatic hexacontatetrachoron page! As is customary we provide full algebraic coordinates.

**1 Sep 2023:**The Polytope of the Month for September is up!

Fixed a rendering bug that caused the animation of the joined pentachoron to lack 3D depth.

**7 Sep 2023:**Fixed a HTML error in the truncated cube page.

### Aug 2023

The polytope of this month is the pentagonal icositetrahedron, the dual of the snub cube and one of the Catalan solids:

This beautiful polyhedron is bounded by 24 non-regular pentagons, 60 edges
(24 long, 36 short), and 36 vertices. Like its dual, the snub cube, its
proportions are closely related to the so-called tribonacci constant

τ, the unique real root of the polynomial:

τ^{3} − τ^{2} − τ − 1 = 0

The ratio of long edges to short edges, for example, is 2/(τ+1) : 1. The chord of each pentagonal face between its two long edges is exactly τ times the length of a short edge.

Find out more on the pentagonal icositetrahedron page! As usual full algebraic coordinates are provided.

**1 Aug 2023:**The Polytope of the Month for August is up!

### Jul 2023

This month we continue with the Catalan solids:

This is the disdyakis dodecahedron, the dual of the great rhombicuboctahedron. Its surface consists of 48 scalene triangles, 72 edges, and 26 vertices. Learn more about it on the disdyakis dodecahedron page! As usual, full Cartesian coordinates are included.

**1 Jul 2023:**The Polytope of the Month for July is up!

**11 Jul 2023:**A little explanation of the name disdyakis dodecahedron.

Renamed

*joined bidecachoron*to joined pentachoron. The earlier naming was apparently a transcription error when borrowing the name from the Polytope Wiki.