A383825 -id:A383825 - cp's OEIS frontend

A383826 Number of polyforms with n cells on the faces of a triakis tetrahedron up to rotation.

1, 1, 2, 3, 5, 7, 14, 16, 23, 18, 7, 1, 1

Offset: 0

Peter Kagey, May 11 2025

These are "one-sided" polyforms.

The triakis tetrahedron is the polyhedral dual of the truncated tetrahedron.

Peter Kagey, Illustration of a(0)-a(4).
Wikipedia, Triakis tetrahedron

Cf. A383825 (free).
Octahedral symmetry: A383799 (row 3), A383801, A383803, A383805, A383807, A383808.
Icosahedral symmetry: A030137, A030138, A383491, A383493, A383495, A383497, A383498, A383786.

A384104 Number of edge-connected components of n faces of the truncated tetrahedron up to the 24 rotations and reflections of the truncated tetrahedron.

Original entry on oeis.org

1, 2, 2, 4, 7, 5, 4, 2, 1

Offset: 0

Peter Kagey, May 19 2025

Two faces are connected if they share an edge.
These are "free" polyforms because both rotations and reflections are allowed.
The truncated tetrahedron is the polyhedral dual of the triakis tetrahedron.

			a(1) = 2 because the truncated tetrahedron is not face-transitive but has two distinct types of faces: triangular faces and hexagonal faces.

Peter Kagey, Illustration of a(1)-a(3).
Wikipedia, Truncated tetrahedron

Cf. A383825 (triakis tetrahedron).

Cf. A384067 (cuboctahedron), A384068 (truncated cube), A384069 (truncated octahedron), A384070 (rhombicuboctahedron), A384071 (cuboctahedron), A384072 (snub cube).

Offset corrected by Pontus von Brömssen, Jun 10 2025

cp's OEIS Frontend

A383826 Number of polyforms with n cells on the faces of a triakis tetrahedron up to rotation.

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