Home
Back
Formula Used:
| From: | To: |
The Midsphere Radius of Tetrakis Hexahedron is the radius of the sphere for which all the edges of the Tetrakis Hexahedron become a tangent line on that sphere. It represents the sphere that touches the midpoints of all edges of the polyhedron.
The calculator uses the formula:
Where:
Explanation: This formula establishes a direct proportional relationship between the height of the Tetrakis Hexahedron and its midsphere radius, with a constant factor of √2/3.
Details: Calculating the midsphere radius is important in geometry and 3D modeling as it helps understand the spatial properties and symmetry of the Tetrakis Hexahedron. It's particularly useful in crystallography, architectural design, and mathematical research involving polyhedral structures.
Tips: Enter the height of the Tetrakis Hexahedron in meters. The value must be positive and greater than zero. The calculator will compute the corresponding midsphere radius using the established mathematical relationship.
Q1: What is a Tetrakis Hexahedron?
A: A Tetrakis Hexahedron is a Catalan solid that can be seen as a cube with square pyramids on each face. It has 24 faces, 36 edges, and 14 vertices.
Q2: How is the midsphere different from the insphere?
A: The midsphere touches the midpoints of all edges, while the insphere is tangent to all faces of the polyhedron.
Q3: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Tetrakis Hexahedron. Other polyhedra have different relationships between their height and midsphere radius.
Q4: What are practical applications of this calculation?
A: This calculation is used in 3D modeling, geometric analysis, architectural design, and in fields that study crystal structures and molecular geometry.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the geometric properties of the Tetrakis Hexahedron, provided the input height is accurate.