## < ⎙ 11 Other formulas that you can solve using the same Inputs

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
Dihedral Angle of Platonic Solids
Dihedral Angle=2*arsin(cos(180/Number of edges meeting at a vertex)/sin(180/Number of edges in a face)) GO
Radius of inscribed sphere inside the regular dodecahedron
Radius of inscribed sphere inside the regular octahedron
Radius of inscribed sphere inside regular tetrahedron
Radius of inscribed sphere inside the cube
Radius of circumscribed sphere in a regular dodecahedron
Radius of circumscribed sphere in a regular icosahedron
Radius of circumscribed sphere in a regular octahedron
Radius of circumscribed sphere in regular tetrahedron
Radius of circumscribed sphere in a cube

## < ⎙ 5 Other formulas that calculate the same Output

Radius of inscribed sphere inside the regular dodecahedron
Radius of inscribed sphere inside the regular icosahedron
Radius of inscribed sphere inside the regular octahedron
Radius of inscribed sphere inside regular tetrahedron
Radius of inscribed sphere inside the cube

### Radius of inscribed sphere inside platonic solids Formula

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))
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
Dihedral Angle of Platonic Solids 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 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

## 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 Radius of inscribed sphere inside platonic solids?

Radius of inscribed sphere inside platonic solids calculator uses 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)) to calculate the Radius, Radius of inscribed sphere inside platonic solids is called the inradius of the platonic solids. Radius and is denoted by r symbol.

How to calculate Radius of inscribed sphere inside platonic solids using this online calculator? To use this online calculator for Radius of inscribed sphere inside platonic solids, enter Dihedral Angle (θ), Number of edges meeting at a vertex (q), Number of edges in a face (p) and Length of edge (a) and hit the calculate button. Here is how the Radius of inscribed sphere inside platonic solids calculation can be explained with given input values -> 0.166673 = 1*0.5*cos(180/3)/(sin(180/3)*tan(180/3)*cos(0.5*1)).

### FAQ

What is Radius of inscribed sphere inside platonic solids?
Radius of inscribed sphere inside platonic solids is called the inradius of the platonic solids and is represented as r=a*0.5*cos(180/q)/(sin(180/p)*tan(180/p)*cos(0.5*θ)) or 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)). A dihedral angle is the angle between two intersecting planes, The number of edges meeting at a vertex in platonic solids, The number of edges in a face of a platonic solid and The Length of edge of polyhedron. .
How to calculate Radius of inscribed sphere inside platonic solids?
Radius of inscribed sphere inside platonic solids is called the inradius of the platonic solids is calculated using 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)). To calculate Radius of inscribed sphere inside platonic solids, you need Dihedral Angle (θ), Number of edges meeting at a vertex (q), Number of edges in a face (p) and Length of edge (a). With our tool, you need to enter the respective value for Dihedral Angle, Number of edges meeting at a vertex, Number of edges in a face and Length of edge and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Radius?
In this formula, Radius uses Dihedral Angle, Number of edges meeting at a vertex, Number of edges in a face and Length of edge. We can use 5 other way(s) to calculate the same, which is/are as follows -