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The Face Diagonal of a Dodecahedron is defined as the distance between any pair of opposite corners on a particular pentagonal face of the Dodecahedron. It represents the longest straight line that can be drawn within a single face of this polyhedron.
The calculator uses the formula:
Where:
Explanation: This formula establishes a direct relationship between the space diagonal (connecting opposite vertices through the 3D space) and the face diagonal (within a single pentagonal face) of a regular dodecahedron.
Details: Calculating the face diagonal is essential for understanding the geometric properties of dodecahedrons, designing structures with this shape, and solving problems in solid geometry and 3D modeling.
Tips: Enter the space diagonal value in meters. The value must be positive and greater than zero. The calculator will compute the corresponding face diagonal using the mathematical relationship between these two dimensions.
Q1: What is a regular dodecahedron?
A: A regular dodecahedron is a three-dimensional shape with 12 identical regular pentagonal faces, 20 vertices, and 30 edges. It is one of the five Platonic solids.
Q2: How is space diagonal different from face diagonal?
A: Space diagonal connects two vertices that are not on the same face (passing through the 3D interior), while face diagonal connects opposite corners within the same pentagonal face.
Q3: Can this formula be used for irregular dodecahedrons?
A: No, this specific formula applies only to regular dodecahedrons where all faces are identical regular pentagons and all angles are equal.
Q4: What are practical applications of dodecahedron geometry?
A: Dodecahedron geometry is used in crystallography, architecture, game design, molecular modeling, and various mathematical and scientific applications.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact for regular dodecahedrons, as it's derived from the fundamental geometric properties of this perfect polyhedron.