Geometry Studies

Here are a few geometry studies that I’ve done to help sharpen my skills. These help with building up an ability to problem solve with 3D shapes in perspective. Many of these are based on the works of the artist Rafael Araujo ( When I used to have an Instagram account, Rafael would generously offer advice to those who were serious about learning. Some of those are available as tutorials on his page there (I no longer know what his handle is though). His tutorials are great because they leave out enough information that you are forced to think for yourself and not just mindlessly follow steps then have no idea what you actually did.

Cubes in perspective, after Rafael Araujo.
Stacked cubes in perspective, after Rafael Araujo, and with cast shadows which I added to the concept to help with figuring out the process for shadows in my perspective drawings.

3D logarithmic spiral, inspired by Rafael’s helix exercise.

Elevated honeycomb shape with cast shadows, after Rafael Araujo.

Dodecahedron in 2-point perspective

Approximation of a sphere using rotated enneagrams.
Based on Rafael Araujo’s “Arches” exercise, but adapted by me to make it a gothic theme and adding cast shadows for practice (plague-ridden monk to the right, erased).
Shadow study of a column and capital (per Architectural Shades and Shadows by Henry McGoodwin, 1904).
Shadow study of a turret and sloped roof (per Architectural Shades and Shadows by Henry McGoodwin, 1904).
Truncated icosahedron in 1-point perspective using Rafael’s calculation box approach.
“The Dance of Earth and Mars”, derived by me and inspired by illustrations in the book Quadrivium (book VI, John Martineau).

Möbius strip, after Rafael Araujo.
Spherical cap, after Rafael Araujo.