Home
Back
Formula Used:
| From: | To: |
The Circumsphere Radius of a Truncated Rhombohedron is the radius of the sphere that contains the polyhedron in such a way that all vertices lie on the sphere's surface. It's an important geometric property in crystallography and materials science.
The calculator uses the formula:
Where:
Explanation: This formula derives from the geometric properties of the truncated rhombohedron and its relationship to the golden ratio.
Details: Calculating the circumsphere radius is crucial for understanding the spatial dimensions of truncated rhombohedra, which appear in crystal structures, quasicrystals, and various nanomaterials.
Tips: Enter the rhombohedral edge length in meters. The value must be positive and non-zero. The calculator will compute the corresponding circumsphere radius.
Q1: What is a truncated rhombohedron?
A: A truncated rhombohedron is a polyhedron obtained by cutting the corners of a rhombohedron, creating new faces at the truncated vertices.
Q2: Where are truncated rhombohedra commonly found?
A: They appear in crystal structures, mineral formations, and architectural designs, particularly in systems with five-fold symmetry.
Q3: How accurate is this formula?
A: The formula is mathematically exact for perfect truncated rhombohedra and provides precise calculations when accurate inputs are given.
Q4: Can this calculator handle different units?
A: The calculator uses meters as the default unit. For other units, convert your measurement to meters before calculation.
Q5: What's the relationship between this formula and the golden ratio?
A: The constants in the formula (√5 specifically) relate to the golden ratio φ = (1+√5)/2, which appears frequently in rhombohedral geometry.