The radius of a circumscribed sphere
of an octahedron is:

, where "a" is the side length

The radius of an inscribed sphere of the octahedron is:

For clarity, the surface area of ​​an octahedron can be represented as a shape net area.

The octahedron surface area can be defined as the area of one of the octahedron's sides. This is the area of a regular triangle, multiplied by 8. Or use the formula:

The volume of the octahedron is:

The radius of a circumscribed sphere
of cube:

, where "a" is the side length 

The radius of an inscribed sphere
of the cube is:

For clarity, the surface area of ​​a cube can be represented as a shape net area.

The cube surface area can be defined as the area of one of the cube's sides. This is the area of a regular quadrilateral (square), multiplied by 6. Or use the formula:

The volume of the cube is:

The radius of a circumscribed sphere
of dodecahedron:

, where "a" is the side length

The radius of an inscribed sphere
of dodecahedron is

For clarity, the surface area of ​​a dodecahedron can be represented as a shape net area.

The dodecahedron surface area can be defined as the area of one of the dodecahedron's sides. This is the area of a regular pentagon, multiplied by 12. Or use the formula:

The volume of the dodecahedron is:

The radius of a circumscribed sphere of the icosahedron:

, where "a" is the side length

The radius of an inscribed sphere of the icosahedron is:

For clarity, the surface area of ​​an icosahedron can be represented as a shape net area.

The icosahedron surface area can be defined as the area of one of the icosahedron's sides. This is the area of a regular triangle, multiplied by 20. Or use the formula:

the volume of the icosahedron is: