Octadecadiminished pentacontatetrapeton

The octadecadiminished pentacontatetrapeton or oddimo, also known as the bitriangular trioprism or triangular trioalterprism, is a convex scaliform polypeton that consists of 18 triangular duoantifastegiaprisms and 54 triangular duoantifastegiums. 6 triangular duoantifastegiaprisms and 12 triangular duoantifastegiums join at each vertex. It can be formed from deleting the vertices of a hexagonal triotegum from a pentacontatetrapeton, that is, removing 18 dodecateric pyramids. It can equivalently be obtained as the convex hull of two tri-orthogonal triangular trioprisms. It is the second member of the bitrioprisms formed from the convex hull of two rotated trioprisms and the only convex scaliform one. It is the second in an infinite family of isogonal triangular dihedral swirlpeta.

Vertex coordinates
The vertices of an octadecadiminished pentacontatetrapeton of edge length 1 are given by:
 * $$±\left(0,\,\frac{\sqrt3}{3},\,0,\,\frac{\sqrt3}{3},\,0,\,\frac{\sqrt3}{3}\right),$$
 * $$±\left(0,\,\frac{\sqrt3}{3},\,0,\,\frac{\sqrt3}{3},\,±\frac12,\,-\frac{\sqrt3}{6}\right),$$
 * $$±\left(0,\,\frac{\sqrt3}{3},\,±\frac12,\,-\frac{\sqrt3}{6},\,0,\,\frac{\sqrt3}{3}\right),$$
 * $$±\left(0,\,\frac{\sqrt3}{3},\,±\frac12,\,-\frac{\sqrt3}{6},\,±\frac12,\,-\frac{\sqrt3}{6}\right),$$
 * $$±\left(±\frac12,\,-\frac{\sqrt3}{6},\,0,\,\frac{\sqrt3}{3},\,0,\,\frac{\sqrt3}{3}\right),$$
 * $$±\left(±\frac12,\,-\frac{\sqrt3}{6},\,0,\,\frac{\sqrt3}{3}\,±\frac12,\,-\frac{\sqrt3}{6}\right),$$
 * $$±\left(±\frac12,\,-\frac{\sqrt3}{6},\,±\frac12,\,-\frac{\sqrt3}{6},\,0,\,\frac{\sqrt3}{3}\right),$$
 * $$±\left(±\frac12,\,-\frac{\sqrt3}{6},\,±\frac12,\,-\frac{\sqrt3}{6},\,±\frac12,\,-\frac{\sqrt3}{6}\right).$$

These coordinates show that an octadecadiminished pentacontatetrapeton can be obtained as the convex hull of two inversely oriented triangular trioprisms.