## < 4 Other formulas that you can solve using the same Inputs

Volume of Platonic Solids
volume=(1/24)*Length of edge^3*Number of edges in a face*Number of faces* cos(180/Number of edges meeting at a vertex)/(sin(180/Number of edges in a face)*tan(180/Number of edges in a face)*tan(180/Number of edges in a face)*cos(0.5*Dihedral Angle)) GO
Radius of inscribed sphere inside platonic solids
Radius=Length of edge*0.5*cos(180/Number of edges meeting at a vertex)/(sin(180/Number of edges in a face)*tan(180/Number of edges in a face)*cos(0.5*Dihedral Angle)) GO
Radius of circumscribed sphere around platonic solids
Radius=Length of edge*0.5*sin(180/Number of edges meeting at a vertex)/(sin(180/Number of edges in a face)*cos(0.5*Dihedral Angle)) GO
Surface Area of Platonic Solids
Surface Area=Length of edge^2*Number of edges in a face*Number of faces*(1/4)*cot(180/Number of edges in a face) GO

### Dihedral Angle of Platonic Solids Formula

Dihedral Angle=2*arsin(cos(180/Number of edges meeting at a vertex)/sin(180/Number of edges in a face))
More formulas
Volume of a Cube GO
Surface Area of a Cube GO
Volume of Regular Dodecahedron GO
Volume of Regular Icosahedron GO
Volume of Regular Octahedron GO
Volume of Regular Tetrahedron GO
Surface Area of Dodecahedron GO
Surface Area of Icosahedron GO
Surface Area of Regular Octahedron GO
Surface Area of Regular Tetrahedron GO
Radius of circumscribed sphere in regular tetrahedron GO
Radius of circumscribed sphere around platonic solids GO
Radius of circumscribed sphere in a cube GO
Radius of circumscribed sphere in a regular octahedron GO
Radius of circumscribed sphere in a regular dodecahedron GO
Radius of circumscribed sphere in a regular icosahedron GO
Radius of inscribed sphere inside platonic solids GO
Radius of inscribed sphere inside the regular octahedron GO
Radius of inscribed sphere inside regular tetrahedron GO
Radius of inscribed sphere inside the regular dodecahedron GO
Radius of inscribed sphere inside the regular icosahedron GO
Surface Area of Platonic Solids GO
Volume of Platonic Solids GO
Edge of Regular Octahedron GO

## What is Dihedral Angle?

Every polyhedron has a dihedral angle at every edge describing the relationship of the two faces that share that edge. This dihedral angle, also called the face angle, is measured as the internal angle with respect to the polyhedron. An angle of 0° means the face normal vectors are antiparallel and the faces overlap each other, which implies that it is part of a degenerate polyhedron. An angle of 180° means the faces are parallel, as in a tiling. An angle greater than 180° exists on concave portions of a polyhedron.

## What are Platonic Solids?

In three-dimensional space, a Platonic solid is a regular, convex polyhedron. It is constructed by congruent (identical in shape and size), regular (all angles equal and all sides equal), polygonal faces with the same number of faces meeting at each vertex. Five solids who meet this criteria are Tetrahedron {3,3} , Cube {4,3} , Octahedron {3,4} , Dodecahedron {5,3} , Icosahedron {3,5} ; where in {p, q}, p represents the number of edges in a face and q represents the number of edges meeting at a vertex; {p, q} is the Schläfli symbol.

## How to Calculate Dihedral Angle of Platonic Solids?

Dihedral Angle of Platonic Solids calculator uses Dihedral Angle=2*arsin(cos(180/Number of edges meeting at a vertex)/sin(180/Number of edges in a face)) to calculate the Dihedral Angle, A dihedral angle of platonic solids is the angle between two intersecting planes. In chemistry, it is the angle between planes through two sets of three atoms, having two atoms in common. In solid geometry, it is defined as the union of a line and two half-planes that have this line as a common edge. In higher dimensions, a dihedral angle represents the angle between two hyperplanes. Dihedral Angle and is denoted by θ symbol.

How to calculate Dihedral Angle of Platonic Solids using this online calculator? To use this online calculator for Dihedral Angle of Platonic Solids, enter Number of edges meeting at a vertex (q) and Number of edges in a face (p) and hit the calculate button. Here is how the Dihedral Angle of Platonic Solids calculation can be explained with given input values -> 0.000352 = 2*arsin(cos(180/0.03)/sin(180/0.03)).

### FAQ

What is Dihedral Angle of Platonic Solids?
A dihedral angle of platonic solids is the angle between two intersecting planes. In chemistry, it is the angle between planes through two sets of three atoms, having two atoms in common. In solid geometry, it is defined as the union of a line and two half-planes that have this line as a common edge. In higher dimensions, a dihedral angle represents the angle between two hyperplanes and is represented as θ=2*arsin(cos(180/q)/sin(180/p)) or Dihedral Angle=2*arsin(cos(180/Number of edges meeting at a vertex)/sin(180/Number of edges in a face)). The number of edges meeting at a vertex in platonic solids and The number of edges in a face of a platonic solid.
How to calculate Dihedral Angle of Platonic Solids?
A dihedral angle of platonic solids is the angle between two intersecting planes. In chemistry, it is the angle between planes through two sets of three atoms, having two atoms in common. In solid geometry, it is defined as the union of a line and two half-planes that have this line as a common edge. In higher dimensions, a dihedral angle represents the angle between two hyperplanes is calculated using Dihedral Angle=2*arsin(cos(180/Number of edges meeting at a vertex)/sin(180/Number of edges in a face)). To calculate Dihedral Angle of Platonic Solids, you need Number of edges meeting at a vertex (q) and Number of edges in a face (p). With our tool, you need to enter the respective value for Number of edges meeting at a vertex and Number of edges in a face and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well. Let Others Know