Home
Back
Midsphere Radius of Rhombic Triacontahedron Formula:
| From: | To: |
The Midsphere Radius of a Rhombic Triacontahedron is the radius of the sphere that is tangent to all the edges of the polyhedron. It represents the sphere that fits perfectly between the inscribed and circumscribed spheres of the shape.
The calculator uses the formula:
Where:
Explanation: This formula calculates the midsphere radius based on the edge length of the rhombic triacontahedron, incorporating the mathematical constant φ (phi) through the expression (5 + √5).
Details: Calculating the midsphere radius is important in geometry and crystallography for understanding the spatial properties of rhombic triacontahedrons, which occur in various natural and synthetic structures.
Tips: Enter the edge length of the rhombic triacontahedron in meters. The value must be positive and greater than zero.
Q1: What is a rhombic triacontahedron?
A: A rhombic triacontahedron is a convex polyhedron with 30 rhombic faces. It is one of the Catalan solids and is the dual polyhedron of the icosidodecahedron.
Q2: How is the midsphere radius different from the insphere radius?
A: The midsphere radius is the radius of the sphere tangent to all edges, while the insphere radius is the radius of the sphere tangent to all faces.
Q3: What are practical applications of this calculation?
A: This calculation is used in crystallography, material science, and geometric modeling where rhombic triacontahedron structures appear.
Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the rhombic triacontahedron. Other polyhedra have different formulas for calculating their midsphere radii.
Q5: What is the relationship between edge length and midsphere radius?
A: The midsphere radius is directly proportional to the edge length, with a constant factor of (5 + √5)/5 ≈ 1.44721.