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The Insphere Radius of Tetrakis Hexahedron is the radius of the sphere that is contained by the Tetrakis Hexahedron in such a way that all the faces just touching the sphere. It represents the largest sphere that can fit inside the polyhedron.
The calculator uses the formula:
Where:
Explanation: The formula establishes a direct relationship between the height of the Tetrakis Hexahedron and the radius of its inscribed sphere, scaled by the constant factor of √5.
Details: Calculating the insphere radius is important in geometry and materials science for understanding the spatial properties of polyhedra, determining packing efficiency, and analyzing the geometric constraints of three-dimensional 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 insphere radius.
Q1: What is a Tetrakis Hexahedron?
A: A Tetrakis Hexahedron is a Catalan solid that can be seen as a cube with square pyramids added to each face. It has 24 isosceles triangular faces.
Q2: How is the height defined for a Tetrakis Hexahedron?
A: The height is the vertical distance from any vertex of the Tetrakis Hexahedron to the face which is directly opposite to that vertex.
Q3: What are typical applications of this calculation?
A: This calculation is used in crystallography, architectural design, and geometric modeling where precise spatial relationships of polyhedra are required.
Q4: Are there limitations to this formula?
A: This formula specifically applies to regular Tetrakis Hexahedrons and assumes perfect geometric proportions.
Q5: Can this calculator handle different units?
A: The calculator uses meters as the default unit. For other units, convert your measurements to meters before calculation.