A063722 -id:A063722 - cp's OEIS frontend

A244055 Number of edges on each face of the Platonic solids (in the order tetrahedron, cube, octahedron, dodecahedron, icosahedron).

3, 4, 3, 5, 3

Offset: 1

Wesley Ivan Hurt, Jun 18 2014

The number of edges on the face of each Platonic solid is a divisor of the total number of edges (A063722) of its corresponding solid. The ratios of the total number of edges to face edges are 6:3, 12:4, 12:3, 30:5, 30:3 --> giving the integer sequence 2, 3, 4, 6, 10.
Although a(n) is also the number of vertices on each face of the Platonic solids, they are not altogether divisors of the total number of vertices (A063723) with the tetrahedron as the only exception. The ratios are 4:3, 8:4, 6:3, 20:5, 12:3.
Please see A053016 for an extensive list of web resources about the Platonic Solids.

Cf. A053016 (faces), A063722 (edges), A063723 (vertices).

A282598 Minimal number of cuts along the edges of n-th Platonic solid required to unfold the net of the solid into the plane, in the order tetrahedron, cube, octahedron, dodecahedron, icosahedron.

Original entry on oeis.org

3, 7, 5, 19, 11

Offset: 1

Felix Fröhlich, Feb 19 2017

An obvious generalization not in the OEIS: Minimal number of cuts along the faces of the cells (i.e. along the 2-faces) of the six Platonic polytopes in four dimensions required to unfold the nets of the polytopes into 3-dimensional space.

Each cut is along an edge, so trivially a(n) <= A063722(n). - Charles R Greathouse IV, Feb 20 2017

Cf. A201187, A063722.

cp's OEIS Frontend

A244055 Number of edges on each face of the Platonic solids (in the order tetrahedron, cube, octahedron, dodecahedron, icosahedron).

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