TIL that an axe blade rotated by 90 degrees (like a hoe) is an "adze"
@nina_kali_nina it's an abbreviation
ADZE stands for Agressive Dissector Z-plane Edge, ADXE and ADYE are for blades in X-plane and Y-plane respectively. Here's a 3d-rendering showing the AD*E axis naming convention.
Axe is just a common misspelling of ADXE, which became acceptable like disk/disc

@hacknorris @nina_kali_nina this one?
https://social.tchncs.de/@kauzerei/116526910180094528

Or do you mean the 4d generalization of Agressive Dissectors where the flat sides of the blade point in ana and kata durections? Wait, are the sides of a 4d axe voluminous, not flat? What dimensionality does the cutting edge has in 4d? Is it flat? Then the sides mus be still flat. But is there four of them I guess?