On the Subject of Johnson Solids

If your Johnson solid for mor 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.

01Square Pyramid47Gyroelongated Pentagonal Cupolarotunda
02Pentagonal Pyramid48Gyroelongated Pentagonal Birotunda
03Triangular Cupola49Augmented Triangular Prism
04Square Cupola50Biaugmented Triangular Prism
05Pentagonal Cupola51Triaugmented Triangular Prism
06Pentagonal Rotunda52Augmented Pentagonal Prism
07Elongated Triangular Pyramid53Biaugmented Pentagonal Prism
08Elongated Square Pyramid54Augmented Hexagonal Prism
09Elongated Pentagonal Pyramid55Parabiaugmented Hexagonal Prism
10Gyroelongated Square Pyramid56Metabiaugmented Hexagonal Prism
11Gyroelongated Pentagonal Pyramid57Triaugmented Hexagonal Prism
12Triangular Bipyramid58Augmented Dodecahedron
13Pentagonal Bipyramid59Parabiaugmented Dodecahedron
14Elongated Triangular Bipyramid60Metabiaugmented Dodecahedron
15Elongated Square Bipyramid61Triaugmented Dodecahedron
16Elongated Pentagonal Bipyramid62Metabidiminished Icosahedron
17Gyroelongated Square Bipyramid63Tridiminished Icosahedron
18Elongated Triangular Cupola64Augmented Tridiminished Icosahedron
19Elongated Square Cupola65Augmented Truncated Tetrahedron
20Elongated Square Cupola66Augmented Truncated Cube
21Elongated Pentagonal Cupola67Biaugmented Truncated Cube
22Elongated Pentagonal Rotunda68Augmented Truncated Dodecahedron
23Gyroelongated Triangular Cupola69Parabiaugmented Truncated Dodecahedron
24Gyroelongated Square Cupola70Metabiaugmented Truncated Dodecahedron
25Gyroelongated Pentagonal Cupola71Triaugmented Truncated Dodecahedron
26Gyroelongated Pentagonal Rotunda72Gyrate Rhombicosidodecahedron
27Gyrobifastigium73Parabigyrate Rhombicosidodecahedron
28Triangular Orthobicupola74Metabigyrate Rhombicosidodecahedron
29Square Orthobicupola75Trigyrate Rhombicosidodecahedron
30Square Gyrobicupola76Diminished Rhombicosidodecahedron
31Pentagonal Orthobicupola77Paragyrate Diminished Rhombicosidodecahedron
32Pentagonal Gyrobicupola78Metagyrate Diminished Rhombicosidodecahedron
33Pentagonal Gyrocupolarotunda79Bigyrate Diminished Rhombicosidodecahedron
34Pentagonal Orthobirotunda80Parabidiminished Rhombicosidodecahedron
35Elongated Triangular Orthobicupola81Metabidiminished Rhombicosidodecahedron
36Elongated Triangular Gyrobicupola82Gyrate Bidiminished Rhombicosidodecahedron
37Elongated Square Gyrobicupola83Tridiminished Rhombicosidodecahedron
38Elongated Pentagonal Orthobicupola84Snub Disphenoid
39Elongated Pentagonal Gyrobicupola85Snub Square Antiprism
40Elongated Pentagonal Orthocuploarotunda86Sphenocorona
41Elongated Pentagonal Gyroc87Augmented Sphenocorona
42Elongated Pentagonal Orthobirotunda88Sphenomegacorona
43Elongated Pentagonal Gyrobirotunda89Hebesphenomegacorona
44Gyroelongated Triangular Bicupola90Disphenocingulum
45Gyroelongated Square Bicupola91Bilunabirotunda
46Gyroelongated Pentagonal Bicupola92Triangular Hebesphenorutuunda