A Johnson solid is a strictly convex polyhedron, each face of which is a regular polygon, but which is not uniform. It is not necessary that each face must be the same polygon, or that the same polygons join around each vertex.

In 1966, Norman Johnson published a list which included all 92 solids, and gave them their names and numbers [1]. He did not prove that there were only 92, but he did conjecture that there were no others. Victor Zalgaller in 1969 proved that Johnson's list was complete.

For more information on the Johnson solids visit Wikipedia - Johnson Solid.

You cannot construct all Johnson solids with Zometool but most of them. When the model contains only struts of one size and color, the model is exact. If the model contains struts of different colors and sizes the model is a close approximation of the Johnson Solid.

The images were rendered in ZomePad. Click on the image to enlarge the view. The ZomePad files, which also include the building instructions, are available for download.

This list of possible zometool models is not complete. This page will be regularly updated and new models will be added (Last update: 14 July 2015).

ca = close approximation

J_{1} - Square Pyramid

J_{2} - Pentagonal Pyramid

J_{3} - Triangular Cupola

J_{4} - Square Cupola (ca)

J_{5} - Pentagonal Cupola

J_{6} - Pentagonal Rotunda

J_{7} - Elongated Triangular Pyramid (ca)

J_{8} - Elongated Square Pyramid (ca)

J_{9} - Elongated Pentagonal Pyramid (ca)

J_{11} - Gyroelongated Pentagonal Pyramid

J_{91} - Bilunabirotunda

Derived Johnson Solids

The Square Pyramid has 5 vertices, 8 edges and 5 faces: 4 triangles, 1 square.

To construct the Square Pyramid, you need:

5

8 (G0, G1 or G2 size)

The Pentagonal Pyramid has 6 vertices, 10 edges and 6 faces: 5 triangles, 1 pentagon.

To construct the Pentagonal Pyramid, you need:

6

10 (B0, B1 or B2 size)

The Triangular Cupola has 9 vertices, 15 edges and 8 faces: 4 triangles, 3 squares, 1 hexagon.

To construct the Triangular Cupola, you need:

9

15 (G0, G1 or G2 size)

The Square Cupola has 12 vertices, 20 edges and 10 faces: 4 triangles, 5 squares, 1 octagon.

To construct the Square Cupola as close approximation, you need:

12

8 (B2)

12 (G1)

The Pentagonal Cupola has 15 vertices, 25 edges and 12 faces: 5 triangles, 5 squares, 1 pentagon, 1 decagon.

To construct the Pentagonal Cupola, you need:

15

25 (B0, B1 or B2 size)

The Pentagonal Rotunda has 20 vertices, 35 edges and 17 faces: 10 triangles, 6 pentagons, 1 decagon.

To construct the Pentagonal Rotunda, you need:

20

35 (B0, B1 or B2 size)

The Elongated Triangular Pyramid has 7 vertices, 12 edges and 7 faces: 4 triangles, 3 squares.

To construct the Elongated Triangular Pyramid as close approximation, you need:

7

3 (Y2)

9 (G1)

The Elongated Square Pyramid has 9 vertices, 16 edges and 9 faces: 4 triangles, 5 squares.

To construct the Elongated Square Pyramid as close approximation, you need:

9

4 (B1)

12 (G1)

The Elongated Pentagonal Pyramid has 11 vertices, 20 edges and 11 faces: 5 triangles, 5 squares, 1 pentagon.

To construct the Elongated Pentagonal Pyramid as close approximation, you need:

11

15 (B1)

5 (R1)

The Gyroelongated Pentagonal Pyramid has 11 vertices, 25 edges and 16 faces: 15 triangles, 1 pentagon.

To construct the Gyroelongated Pentagonal Pyramid, you need:

11

25 (B0, B1 or B2 size)

The Bilunabirotunda has 14 vertices, 26 edges and 14 faces: 8 triangles, 2 squares, 4 pentagons. See this YouTube video for the construction and animated views of the Bilunabirotunda.

To construct the Bilunabirotunda, you need:

14

26 (B0, B1 or B2 size)

The "6 Bilunabirotundae around a cube" has 56 vertices, 120 edges and 54 faces: 24 triangles, 6 squares, 24 pentagons. See this YouTube video for the construction and animated views of the 6 Bilunabirotundae model.

To construct the "6 Bilunabirotundae around a cube", you need:

56

120 (B0, B1 or B2 size)

[1] Johnson, Norman W. (1966), "Convex polyhedra with regular faces", Canadian Journal of Mathematics 18: 169-200