On the Subject of Johnson Solids

If your Johnson solid for more than four hours you should see a doctor.

On the module is one polyhedron which is a member of the Johnson solids. To defuse the module, you must name it and input its corresponding number into the module.

The polyhedron may be hidden by pressing the J. Pressing the J again will cause the polyhedron to become visible again.

Finding Its Name

The Johnson solids fall into three main types: Pyramids, cupolae and rotundae, Modified uniform solids, and Elementary solids.

Pyramids, cupolae, and rotundae

Solids in this category are one of the eponymous pyramids, cupolae, or rotundae, or a modification of one or more of them.

All sections of a solid’s name should be ordered by appearance in this list:

• Elongated: having a ring of squares separating two halves.
• Gyroelongated: having a ring of alternating triangles separating two halves.
• Triangular: using a triangle.
• Square: using a square.
• Pentagonal: using a pentagon.
• Gyro-: having one half gyrated (twisted), indicated by their main polygon.
• Ortho-: not having one half gyrated (twisted).
  • Ortho- is only used when a cupola or rotunda is opposite another.
• Bi-: having two instances of.
• Pyramid: having a polygon surrounded by triangles which converge to a single point.
• Cupola: having a polygon surrounded by alternating squares and triangles.
  • The digonal cupola, also known as a triangular prism, is referred to as a fastigium.
• Rotunda: having a polygon surrounded by triangles and pentagons.
  • If both a cupola and a rotunda appear in the solid, both names are used.

Modified uniform solids

Solids in this category are created by augmenting, diminishing, and/or gyrating an existing uniform solid.

Sections of a solid’s name should be ordered by appearance in this list:

• Para-: happening on opposite sides of the solid.
• Meta-: not happening on opposite sides of the solid.
• Bi-: happening twice.
• Tri-: happening three times.
• Augmented: having a pyramid or cupola attached to one side.
  • Augmented is the inverse of Diminished, but both can be applied.
• Gyrate: having a section gyrated (twisted).
  • Diminished: having a section removed and replaced with a polygon.
  • The prefixes Bi- and Tri- can appear after Augmented or Gyrate when directly applied to Diminished.

The uniform solid is one of the following unfolded polyhedra:

Triangular Prism	Pentagonal Prism	Hexagonal Prism

Dodecahedron	Icosahedron	Rhombicosidodecahedron

Truncated Tetrahedron	Truncated Cube	Truncated Dodecahedron

Elementary solids

Solids in this category cannot be constructed in the ways outlined above.

Sections of a solid’s name should be ordered by appearance in this list:

• Augmented: having a pyramid attached to one side.
• Triangular: Exact meaning unclear: use if the solid has a hexagon.
• Bi-: having two instances of.
• Luna-: a square with triangles on opposite sides.
  • If there are three instances, use Hebespheno- instead.
  • Otherwise, if there are two neighboring instances, use Spheno- to refer to the resulting compound.
  • Use Di- instead of Bi- to prefix Spheno-.
• Cingulum: related to Gyroelongated; having a ring of alternating triangles.
• Corona: having a “crown” of 8 triangles.
• Megacorona: having a “crown” of 12 triangles.
  • Corona and Megacorona do not count triangles that are part of a Luna.
• Rotunda: referring to a section of a pentagonal rotunda, notably a vertex surrounded by two triangles and two pentagons alternating.

Two solids do not fit with the rest. They have been unfolded below.

Snub Disphenoid	Snub Square Antiprism

Finding Its Number

Each Johnson solid was assigned a number by Norman Johnson himself.

To solve the module, set the display to the number to the left of the solid’s name and press the button labelled SUBMIT. An incorrect input will cause a strike.

01	Square Pyramid	47	Gyroelongated Pentagonal Cupolarotunda
02	Pentagonal Pyramid	48	Gyroelongated Pentagonal Birotunda
03	Triangular Cupola	49	Augmented Triangular Prism
04	Square Cupola	50	Biaugmented Triangular Prism
05	Pentagonal Cupola	51	Triaugmented Triangular Prism
06	Pentagonal Rotunda	52	Augmented Pentagonal Prism
07	Elongated Triangular Pyramid	53	Biaugmented Pentagonal Prism
08	Elongated Square Pyramid	54	Augmented Hexagonal Prism
09	Elongated Pentagonal Pyramid	55	Parabiaugmented Hexagonal Prism
10	Gyroelongated Square Pyramid	56	Metabiaugmented Hexagonal Prism
11	Gyroelongated Pentagonal Pyramid	57	Triaugmented Hexagonal Prism
12	Triangular Bipyramid	58	Augmented Dodecahedron
13	Pentagonal Bipyramid	59	Parabiaugmented Dodecahedron
14	Elongated Triangular Bipyramid	60	Metabiaugmented Dodecahedron
15	Elongated Square Bipyramid	61	Triaugmented Dodecahedron
16	Elongated Pentagonal Bipyramid	62	Metabidiminished Icosahedron

17	Gyroelongated Square Bipyramid	63	Tridiminished Icosahedron
18	Elongated Triangular Cupola	64	Augmented Tridiminished Icosahedron
19	Elongated Square Cupola	65	Augmented Truncated Tetrahedron
20	Elongated Pentagonal Cupola	66	Augmented Truncated Cube
21	Elongated Pentagonal Rotunda	67	Biaugmented Truncated Cube
22	Gyroelongated Triangular Cupola	68	Augmented Truncated Dodecahedron
23	Gyroelongated Square Cupola	69	Parabiaugmented Truncated Dodecahedron
24	Gyroelongated Pentagonal Cupola	70	Metabiaugmented Truncated Dodecahedron
25	Gyroelongated Pentagonal Rotunda	71	Triaugmented Truncated Dodecahedron
26	Gyrobifastigium	72	Gyrate Rhombicosidodecahedron
27	Triangular Orthobicupola	73	Parabigyrate Rhombicosidodecahedron
28	Square Orthobicupola	74	Metabigyrate Rhombicosidodecahedron
29	Square Gyrobicupola	75	Trigyrate Rhombicosidodecahedron
30	Pentagonal Orthobicupola	76	Diminished Rhombicosidodecahedron
31	Pentagonal Gyrobicupola	77	Paragyrate Diminished Rhombicosidodecahedron
32	Pentagonal Orthocupolarotunda	78	Metagyrate Diminished Rhombicosidodecahedron

33	Pentagonal Gyrocupolarotunda	79	Bigyrate Diminished Rhombicosidodecahedron
34	Pentagonal Orthobirotunda	80	Parabidiminished Rhombicosidodecahedron
35	Elongated Triangular Orthobicupola	81	Metabidiminished Rhombicosidodecahedron
36	Elongated Triangular Gyrobicupola	82	Gyrate Bidiminished Rhombicosidodecahedron
37	Elongated Square Gyrobicupola	83	Tridiminished Rhombicosidodecahedron
38	Elongated Pentagonal Orthobicupola	84	Snub Disphenoid
39	Elongated Pentagonal Gyrobicupola	85	Snub Square Antiprism
40	Elongated Pentagonal Orthocupolarotunda	86	Sphenocorona
41	Elongated Pentagonal Gyrocupolarotunda	87	Augmented Sphenocorona
42	Elongated Pentagonal Orthobirotunda	88	Sphenomegacorona
43	Elongated Pentagonal Gyrobirotunda	89	Hebesphenomegacorona
44	Gyroelongated Triangular Bicupola	90	Disphenocingulum
45	Gyroelongated Square Bicupola	91	Bilunabirotunda
46	Gyroelongated Pentagonal Bicupola	92	Triangular Hebesphenorotunda