Pentagonal Cube Math

The following formulas show the measurements for the face of a perfect crystal which is rarely found in nature.

Pentagonal cube math. Select the type color printer friendly. The pentagon has three short edges of unit length each and two long edges of length. The acute angle is between the two long edges. The dihedral angle equals arccos 1 t 2 2 136 309 232 892 32 displaystyle arccos 1 t 2 2 approx 136 309 232 892 32 circ.

From an aerial view it looks like a pentagon. Like other polygons a pentagon can be classified as regular or irregular. The diagonals of a convex regular pentagon are in the golden ratio to its sides. The acute angle is between the two long edges.

Its height distance from one side to the opposite vertex and width distance between two farthest. Know the properties of a cube by working closely with this printable chart that puts everything in a nutshell. A regular pentagon has five lines of reflectional symmetry and rotational symmetry of order 5 through 72 144 216 and 288. In the figure below are 3 different types of pentagons.

Displaystyle r m a frac phi 2 2 where ϕ is the golden ratio. A regular pentagon has schläfli symbol 5 and interior angles are 108. R m a ϕ 2 2. In pyritohedral pyrite the faces have a miller index of 210 which means that the dihedral angle is 2 arctan 2 126 87 and each pentagonal face has one angle of approximately 121 6 in between two angles of approximately 106 6 and opposite two angles of approximately 102 6.

A pentagon is a five sided polygon. Note that given a regular dodecahedron of edge length one ru is the radius of a circumscribing sphere about a cube of edge length ϕ and ri is the apothem of a regular pentagon of edge length ϕ.