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Midsphere Radius of Pentagonal Icositetrahedron Formula:
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The Midsphere Radius of Pentagonal Icositetrahedron is the radius of the sphere for which all the edges of the Pentagonal Icositetrahedron become a tangent line on that sphere. It represents the sphere that is tangent to all edges of the polyhedron.
The calculator uses the formula:
Where:
Explanation: The formula calculates the midsphere radius based on the snub cube edge length and the mathematical constant Tribonacci_C, which is fundamental to the geometry of pentagonal icositetrahedron.
Details: Calculating the midsphere radius is important in geometric modeling, crystallography, and understanding the spatial properties of the pentagonal icositetrahedron. It helps in determining the sphere that touches all edges of this complex polyhedron.
Tips: Enter the Snub Cube Edge length in meters. The value must be positive and greater than zero for accurate calculation.
Q1: What is a Pentagonal Icositetrahedron?
A: A Pentagonal Icositetrahedron is a Catalan solid that is the dual of the snub cube, consisting of 24 identical irregular pentagonal faces.
Q2: What is the Tribonacci constant?
A: The Tribonacci constant is the real root of the equation x³ = x² + x + 1, approximately equal to 1.839286755214161, which appears in various geometric contexts.
Q3: How is the midsphere different from the insphere?
A: The midsphere is tangent to all edges of the polyhedron, while the insphere is tangent to all faces. They represent different geometric properties of the shape.
Q4: What are typical values for the midsphere radius?
A: The midsphere radius depends on the size of the polyhedron. For a standard snub cube edge length of 1 unit, the midsphere radius is approximately 0.5 units.
Q5: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the pentagonal icositetrahedron due to its unique geometric properties and relationship with the Tribonacci constant.