Convex

The convex neoplatonic solids.

The eight without coplanar faces

Convex with no two adjacent faces coplanar — identified by Rausenberger, and later by Freudenthal and van der Waerden. Forbidding coplanar faces is an arbitrary conditioning, and a wrong road: it ends the story at eight, where the convex family below begins. (The triangular bipyramid is non-prime; no matter.)

v4CCAE v=4 · tetrahedron

v5CCACAE v=5 · triangular bipyramid

v6CCCACAAE v=6 · octahedron

v7CCCACACAAE v=7 · pentagonal bipyramid

v8CCCACACACAAE v=8 · snub disphenoid

v9CCCACCACACAAAE v=9 · triaugmented triangular prism

v10CCCACCACACAACAAE v=10 · gyroelongated square bipyramid

v12CCCCACCACACACAACAAAE v=12 · icosahedron

The convex family

Every bend nonnegative, coplanar faces welcome — all 47 among the 79349 prime nets with v ≤ 30 (pancakes, the doubly covered flat case, are listed separately).

v10CCCACACACCAACAAE v=10

v11CCCACCACACACACAAAE v=11

v12CCCACCACCACACACAAAAE v=12

v13CCCACCACACCACACACAAABE v=13

v14CCCACACACCAACACACCAACAAE v=14

v14CCCCACCACACACACACAACAAAE v=14

v15CCCCACCACACACACACACAACAAAE v=15

v16CCCACCACACCACACACAACACAACAAE v=16

v16CCCCACCACACCACACACACAACAAAAE v=16

v18CCCACACACCAACACACCAACACACCAACAAE v=18

v18CCCACCCACCACCACACCAACAACAADECAAE v=18

v18CCCCACCACACACCACACACACAACACAAABE v=18