Studies of polyhedra: bodies of many faces
Semiregular solids formed by truncating the cube, counted by their triangular, square, hexagonal and pentagonal faces
The sheet is filled with drawings of polyhedra — truncated and faceted solids — each annotated with the number and kind of its faces: octagons, squares, hexagons, triangles and pentagons. Several notes explain how a body is generated by cutting the corners of a cube back to the middle of each edge, or by subdividing hexagonal faces into six equilateral triangles, producing bodies of 14, 16, 50, 132, 152 or 198 faces. Two solids at the foot of the sheet are sketched in red chalk, including a spiky stellated form and a truncated body.
On this page
Truncating the cube to make a fourteen-faced body
A body of 14 faces — 8 octagonal and 6 triangular — is drawn from the die (cube) by taking off its corners. The general recipe is given at the end: cut the corners of the cube down to the middle of each edge.
A body of 152 faces and an icosidodecahedral form
One solid is counted as 152 faces — 80 triangular, 60 square and 12 pentagonal. A neighbouring note records a body of 20 triangles and 12 pentagons, and a 32-faced body of 20 hexagons and 12 pentagons.
Counting the faces: 198 = 192 triangles + 6 squares
The left column tallies a body of 198 faces, that is 192 triangles and 6 squares, alongside further face-counts (24, 8, 192, 60, 12). A lower note reckons 132 faces as 12 pentagons and 120 triangles, six for each of the twenty hexagons.