So in those two pages of big dice collections, I'e found these ones of the four infinite axial families:

- Bipyramids: 3-8, 14, 16, 18
- Trapezohedra: 3-7, 9, 11, 13, 17, 25
- Prisms: 3-20
- Antiprisms: 2-6, 8, 10

The small index values are well-represented, while the larger ones are scattered.

Prismatic and antiprismatic dice are sometimes called rolling-pin and rolling-log dice. Many of them have rounded or pyramidal endcaps, to keep the dice from landing on them. The regular icosahedron is a 5-antiprism with pyramidal endcaps.

I spent some time searching for "rpg dice" and "d&d dice" and "crystal dice" in shapefile archives for 3D printers. I found some Braille dice and lots of dice boxes, including some icosahedral ones. DOTS RPG Project has Braille-dotted versions of a 4-prism, a cube, an octahedron, a 5-trapezohedron, a dodecahedron, and an icosahedron: d4, d6, d8, d10, d12, d20, and Screw Top D20 Dice Box by StormCrow13 - Thingiverse

A common variation of 5-trapezohedron dice is to have two of them for do, one as the ones digit: 0, 1, 2, ..., 9, and one as the tens digit: 0, 10, 20, ..., 90.

- Dice store - Shop game dice for sale, bulk dice, D&D dice sets, playing cards, dice games, game supplies - has the Platonic solids, 5-trapezohedra, 8-bipyramids, and d30 rhombic triacontahedra (rhombi on icosahedron).
- Welcome to Dice Depot - has the Platonic solids, 3- and 5-prisms, 5- and 7-trapezohedra, 8-bipyramids, and d24 tetrakis hexahedra (pyramids on cube)
- Facets Dice - Full set of custom RPG dice by sablebadger - Thingiverse -- this page has a 10-bipyramid, two 5-trapezohedra, and 2-, 3-, and 4-antiprisms. The 2-antiprism is an isosceles tetrahedron, one that has been stretched in one direction.
- Alternate d20 by south2012 - Thingiverse - a 10-bipyramid.
- Customizable Crystal Dice by silvereye - Thingiverse - 3- to 10-antiprisms. I've found some other sets of such dice: mostly of 3-, 4-, 5-, 6-, and 10-antiprisms.
- Crystal Dice Set for Tabletop by Billie Ruben - Thingiverse has a 4-prism, a 6-prism, half an 8-bipyramid, a 5-trapezohedron, and a 6-antiprism
- D60 by hyperspacedesign - Thingiverse - deltoidal hexecontahedron (kites on icosahedron)
- 3D Printable D3 - Three Sided Dice by Christopher Kettle - a 3-prism

With them added in, I have

- Bipyramids: 3-8, 10, 14, 16, 18
- Trapezohedra: 3-7, 9, 11, 13, 17, 25
- Prisms: 3-20
- Antiprisms: 2-10

It seems to me that one may be able to write a program that generates shapefiles for 3D-printed dice.