A pyramid is formed by adding a point the apex over a polygon and erecting triangles connecting the point to the edges of the polygon. A cupola is formed by placing a polygon and its Stott expansion on parallel planes and connecting them with triangles and squares. A rotunda is a hemispherical dome-shaped polyhedron; there is only one in Johnson's list: the pentagonal rotunda, J6.
The next solids in Johnson's list are formed by pasting together various combinations of the first six plus some prisms and antiprisms. The list is quite long due to combinatorial explosion.
The prefix ortho- means two parts are in matching orientation; whereas gyro- means one part rotated with respect to the other. Thus, an elongation or gyroelongation is the lengthening of a polyhedron by attaching or inserting a prism or antiprism, respectively.
A fastigium is a roof-like shape, referring to a triangular prism in J These are the only chiral Johnson solids. Next are augmentations of the polygonal prisms.
An augmentation is the attaching of one or more smaller polyhedra usually pyramids or cupolae to a larger one. There is some overlap between this category and the previous one, but we list them separately here because their 4D analogues, the duoprism augmentations, form their own category of CRFs. Wells, D. London: Penguin, pp. New York: Penguin Books, pp. Zalgaller, V. Convex Polyhedra with Regular Faces.
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J02 - Pentagonal Pyramid. J03 - Triangular Cupola. J04 - Square Cupola. J05 - Pentagonal Cupola. J06 - Pentagonal Rotunda. GJ06 - "Great" Pentagonal Rotunda. J07 - Elongated Triangular Pyramid. J08 - Elongated Square Pyramid.
J09 - Elongated Pentagonal Pyramid. J10 - Gyroelongated Square Pyramid. J11 - Gyroelongated Pentagonal Pyramid. GJ11 - Diminished Great Icosahedron. J12 - Triangular Dipyramid. J13 - Pentagonal Dipyramid. J14 - Elongated Triangular Dipyramid. J15 - Elongated Square Dipyramid. J16 - Elongated Pentagonal Dipyramid. J17 - Gyroenlongated Square Dipyramid. J18 - Elongated Triangular Cupola. J19 - Elongated Square Cupola. J20 - Elongated Pentagonal Cupola. J21 - Elongated Pentagonal Rotunda.
J22 - Gyroelongated Triangular Cupola. J23 - Gyroelongated Square Cupola. J24 - Gyroelongated Pentagonal Cupola. J25 - Gyroelongated Pentagonal Rotunda. J26 - Gyrobifastigium.
J27 - Triangular Orthobicupola. J28 - Square Orthobicupola. J29 - Square Gyrobicupola. J30 - Pentagonal Orthobicupola. GJ30 - "Great" Pentagonal Orthobicupola. J31 - Pentagonal Gyrobicupola. J32 - Pentagonal Orthocupolarotunda.
J33 - Pentagonal Gyrocupolarotunda. J34 - Pentagonal Orthobirotunda. GJ34 - "Great" Pentagonal Orthobirotunda. J35 - Elongated Triangular Orthobicupola. J36 - Elongated Triangular Gyrobicupola. J38 - Elongated Pentagonal Orthobicupola. J39 - Elongated Pentagonal Gyrobicupola.
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