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The Snub Cube Edge of Pentagonal Icositetrahedron is the length of any edge of the Snub Cube of which dual body is the Pentagonal Icositetrahedron. This geometric relationship is fundamental in understanding the properties of these polyhedral forms.
The calculator uses the mathematical formula:
Where:
Explanation: This formula establishes the relationship between the insphere radius of a pentagonal icositetrahedron and the edge length of its dual snub cube, using the mathematical constant known as the Tribonacci constant.
Details: Understanding the relationship between dual polyhedra is crucial in geometry and crystallography. This calculation helps in determining geometric properties and spatial relationships between these complex three-dimensional shapes.
Tips: Enter the insphere radius of the pentagonal icositetrahedron in meters. The value must be positive and non-zero. The calculator will compute the corresponding snub cube edge length.
Q1: What is the Tribonacci constant?
A: The Tribonacci constant is the real root of the equation x³ - x² - x - 1 = 0, approximately equal to 1.839286755214161.
Q2: What is a dual polyhedron?
A: In geometry, polyhedra are associated in pairs called duals, where the vertices of one correspond to the faces of the other.
Q3: What are the applications of this calculation?
A: This calculation is used in mathematical geometry, crystallography, and the study of polyhedral structures and their properties.
Q4: Are there limitations to this formula?
A: This formula specifically applies to the relationship between pentagonal icositetrahedron and its dual snub cube, and may not be applicable to other polyhedral forms.
Q5: What units should be used for input?
A: The calculator uses meters as the unit of measurement, but the formula is dimensionally consistent and will work with any consistent unit system.