In regards to of a spherical, outer event horizon surface ---planckian area-- being equal to the the four great circles that define a spherical cubo-octahedron, this below is presented this Oloid of two same size circles --ergo same area-- reshaped as an The Oloid below at link.
For me it is perhaps another way of beginning to giving volume to a black hole via four great circle areas of the cubo-octahedron. That part is still and unknown. Anyway here is the link to The OLoid on Instagram. I dunno anything about accuracy of the claims.
...' That property leads to a surprising result. When unrolled, the oloid’s surface area equals exactly 4πr², the same formula as a sphere of the same radius. The shape and curvature are completely different, but the total area matches precisely because of how the perpendicular circles and straight generators distribute area across the surface. '..
https://www.instagram.com/reel/DVeLY52AfIy/?igsh=YzljYTk1ODg3Zg%3D%3D

