Formula Used:
From: | To: |
The Circumsphere Radius of a Truncated Icosidodecahedron is the radius of the sphere that contains the polyhedron such that all vertices lie on the sphere's surface. It is a key geometric property of this Archimedean solid.
The calculator uses the formula:
Where:
Explanation: This formula establishes the mathematical relationship between the circumsphere radius and midsphere radius of a truncated icosidodecahedron, derived from its geometric properties.
Details: Calculating the circumsphere radius is essential for understanding the spatial dimensions and geometric properties of truncated icosidodecahedrons, which have applications in crystallography, architecture, and mathematical modeling.
Tips: Enter the midsphere radius value in meters. The value must be positive and non-zero. The calculator will compute the corresponding circumsphere radius using the established mathematical relationship.
Q1: What is a Truncated Icosidodecahedron?
A: A truncated icosidodecahedron is an Archimedean solid with 120 vertices, 180 edges, and 62 faces (30 squares, 20 regular hexagons, and 12 regular decagons).
Q2: What is the difference between circumsphere and midsphere?
A: The circumsphere passes through all vertices of the polyhedron, while the midsphere is tangent to all edges of the polyhedron.
Q3: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to truncated icosidodecahedrons as it's derived from their unique geometric properties.
Q4: What are practical applications of this calculation?
A: This calculation is used in mathematical research, 3D modeling, architectural design, and in understanding the geometric properties of complex polyhedra.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact, though practical implementations may have minor rounding errors depending on the precision of input values and computational methods.