Escher Geometric Shapes and Solids

This page is inspired by M.C. Escher's artwork based on geometry.

M.C. Escher's Study for Stars Shapes

image image Escher's Study for Stars (left)
Escher's Stars (right)

The shapes are the frames of polyhedrons, which are three-dimensional figures with straight edges and sharp vertices, and flat faces that are polygons.

  1. An octahedron compounded with a cube. It is a polyhedral stellation.
  2. Tetrahedron, also known as a triangular pyramid.
  3. Compound of three octahedrons or octahedron 3-compound or sometimes called Escher's solid.
  4. Rhombic dodecahedron which has 12 rhombus shaped faces.
  5. Regular icosahedron a polyhedron with 20 faces that are regular triangles, equilaterals. Escher's sketch is similar to the one drawn by Leonardo da Vinci. There are 20 sided dice used in role-playing games like Dungeons & Dragons.
  6. Octahedron, two pyramids matched at their square bases.
  7. Cube
  8. Stellated octahedron which is a compound of two tetrahedrons.
  9. Regular dodecahedron which has twelve flat regular pentagon faces.
  10. Two compound cubes. One rotated 45o away from the other at two directions.

The base shapes are ancient. They include Plato's five Platonic solids: tetrahedron, cube, regular octahedron, dodecahedron, and icosahedron. Johannes Kepler also drew five Platonic solids in his book Harmonice Mundi.

4-Cube from Escher Art

Progression from art to CAD drawing:
1) Escher Stars 2) Cube extracted and rotated 3) CAD design with no hidden lines
image image image
1) Escher Study for Stars 2) Cube extracted and rotated 3) CAD design, no inner lines
image image image
1) Rhombic dodecahedron 2) CAD, Rhombic dodecahedron 3) CAD rotated(different CAD program)
image image image

Searching for Escher Art 4-Cube Description

Google Search

Question, What are the shapes in Escher's stars study?

Google AI posted the correct image:
image
Escher's "Stars" (1948) features a compound of three interlocking octahedra in the center, with other geometric shapes like the Stella Octangula (a compound of two tetrahedra) and a compound of a cube and octahedron floating in the background. The artwork also includes smaller versions of all five Platonic solids, the rhombic dodecahedron, and other polyhedra. Central and prominent shapes
Compound of three octahedra: This is the largest and most prominent shape in the center of the work, made of three interlocking octahedra. Stella Octangula: Also known as the star tetrahedron, this is the compound of two tetrahedra that appears prominently in the upper right. Compound of a cube and octahedron: Featured in the upper left, this is a shape where a cube and an octahedron are combined. Compound of two cubes: This shape is shown in the lower left, with two cubes sharing a common axis.
Other shapes included
Platonic solids: All five Platonic solids are represented in smaller forms throughout the piece. Rhombic dodecahedron: This shape also appears, along with other less common polyhedra like the cuboctahedron and rhombicuboctahedron.

ChatGPT prompt

Here is a link to the image of Escher's study of his stars drawing. What are the shapes in this image?

Here are the major polyhedral shapes in Study for Stars (1948) by M. C. Escher — the preparatory drawing for his print “Stars”.
...Image of "Study" and image of "Stars".
Below are the key shapes identified, with commentary on each:
Stellated rhombic dodecahedron (also called “Escher’s solid”)
In the Study for Stars this is the largest polyhedron shown, drawn in wire-frame form. Wikipedia +2 Wikipedia +2
It is a stellation of the rhombic dodecahedron (i.e., its faces are “puffed out” into star-like forms) and sometimes described as a compound of three flattened octahedra. Wikipedia +1
Although in the final print “Stars” the central cage becomes the compound of three octahedra, in the Study for Stars this stellated rhombic dodecahedron is prominent. Wikipedia
Compound of three octahedra
This is the polyhedron that becomes the central “cage” in the final “Stars” print (with the two chameleons inside). Wikipedia +1
In the study drawing it appears among the floating wire-frame solids (though the largest form is the stellated rhombic dodecahedron).
It consists of three regular octahedra sharing the same centre and oriented symmetrically. Wikipedia
Stella octangula (compound of two tetrahedra)
One of the smaller polyhedral forms in the study (and also appears in the final “Stars” print, upper right). Wikipedia
This compound has the shape of an 8-pointed star in 3D — two interpenetrating tetrahedra.
Other regular and semi-regular polyhedra / compounds
The drawing includes various floating wire-frame solids: likely the five Platonic solids (tetrahedron, cube, octahedron, dodecahedron, icosahedron) and several star-polyhedra or stellations. platonicrealms.com +1
Some sources specifically mention that Escher’s study shows “regular polyhedra, including dodecahedrons and icosahedrons”.
Also likely included: the compound of cube and octahedron, or other Archimedean/stellated forms, as preliminary explorations of forms he used in “Stars”.
Summary
In short: the Study for Stars is packed with geometric experimentation — it does not just show one shape, but many: major compounds (like the compound of three octahedra), stellated solids (like the stellated rhombic dodecahedron), and classic regular solids/compounds. Escher was exploring “floating star-shapes” in space, mixing order (geometry) and chaos (floating, skewed orientation). Wikipedia +1

Marked Shapes in the Drawing of Escher Study for Stars

Escher Stars Escher Study for Stars
Images from: wikiart.org. Fair Use, for example: the image is only being used for informational and educational purposes.