1D Line
2D
Regular Polygons: Equilateral Triangle , Square , Pentagon , Hexagon , Heptagon , Octagon , Nonagon , Decagon , Hendecagon , Dodecagon , Hexadecagon , N-gon , Polygon Ring
Other Polygons: Triangle , Right Triangle , Isosceles Triangle , IR Triangle , Quadrilateral , Rectangle , Rhombus , Parallelogram , Right Kite , Kite , Right Trapezoid , Isosceles Trapezoid , Trapezoid , Cyclic Quadrilateral , Tangential Quadrilateral , Arrowhead , Concave Quadrilateral , Antiparallelogram , House-Shape , Symmetric Pentagon , Concave Pentagon , Parallelogon , Arrow-Hexagon , Sharp Kink , Frame , Threestar , Fourstar , Pentagram , Hexagram , Unicursal Hexagram , Cross , Oktagram , Star of Lakshmi , Polygon
Round Forms: Circle , Semicircle , Circular Sector , Circular Segment , Circular Layer , Round Corner , Circular Corner , Annulus , Annulus Sector , Curved Rectangle , Ellipse , Semi-Ellipse , Elliptical Segment , Elliptical Sector , Stadium , Digon , Spherical Triangle , Spiral , Log. Spiral , Reuleaux Triangle , Cycloid , Astroid , Hypocycloid , Cardioid , Epicycloid , Parabolic Segment , Arbelos , Salinon , Lune , Three Circles , Polycircle , Oval , Lemniscate , Squircle
3D
Platonic Solids: Tetrahedron , Cube , Octahedron , Dodecahedron , Icosahedron
Archimedean Solids: Truncated Tetrahedron , Cuboctahedron , Truncated Cube , Truncated Octahedron , Rhombicuboctahedron , Truncated Cuboctahedron , Icosidodecahedron , Truncated Dodecahedron , Truncated Icosahedron , Snub Cube
Catalan Solids: Triakis Tetrahedron , Rhombic Dodecahedron , Triakis Octahedron , Tetrakis Hexahedron , Deltoidal Icositetrahedron , Hexakis Octahedron , Rhombic Triacontahedron , Triakis Icosahedron , Pentakis Dodecahedron , Pentagonal Icositetrahedron
Johnson Solids: Pyramids , Cupolae , Rotunda , Elongated Pyramids , Snub Disphenoid
Other Polyhedrons: Cuboid , Square Pillar , Triangular Pyramid , Square Pyramid , Regular Pyramid , Pyramid , Regular Frustum , Frustum , Bipyramid , Bifrustum , Ramp , Right Wedge , Wedge , Rhombohedron , Parallelepiped , Prism , Oblique Prism , Antiprism , Prismatoid , Trapezohedron , Disphenoid , Corner , General Tetrahedron , Wedge-Cuboid , Half Cuboid , Skewed Cuboid , Skewed Three-Edged Prism , Truncated Rhombohedron , Hollow Cuboid , Hollow Pyramid , Stellated Octahedron , Small Stellated Dodecahedron , Great Stellated Dodecahedron
Round Forms: Sphere , Hemisphere , Cylinder , Cut Cylinder , Oblique Cylinder , Generalized Cylinder , Cone , Truncated Cone , Oblique Circular Cone , Elliptic Cone , Bicone , Spheroid , Ellipsoid , Semi-Ellipsoid , Spherical Sector , Spherical Cap , Spherical Segment , Spherical Wedge , Cylindrical Wedge , Cylindrical Sector , Cylindrical Segment , Flat End Cylinder , Spherical Shell , Cylindrical Shell , Hollow Cone , Truncated Hollow Cone , Spherical Ring , Torus , Spindle Torus , Arch , Reuleaux-Tetrahedron , Capsule , Lens , Barrel , Egg Shape , Paraboloid , Hyperboloid , Oloid , Steinmetz Solids
4D
Tesseract , Hypersphere
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Pentakis Dodecahedron Calculator
Calculations in a pentakis dodecahedron, the dual body of the truncated icosahedron . A pentakis dodecahedron is a polyhedron with isosceles triangle faces with legs a and base b. Five of these are attached as a pyramid on each face of a dodecahedron with edge length b. Enter one value and choose the number of decimal places. Then click Calculate.

Formulas:
b = 3/38 * ( 9 + √5 ) * a
A = 15/19 * a² * √ 413 + 162√5
V = 15/76 * a³ * ( 23 + 11√5 )
r_{m} = a/4 * ( 3 + √5 )
r_{i} = 3/2 * a * √ ( 81 + 35√5 ) / 218
A/V = 76/19 * √ 413 + 162√5 / ( a * √ 23 + 11√5 )

The pentakis dodecahedron is a Catalan solid. Edge lengths and radiuses have the same unit (e.g. meter), the area has this unit squared (e.g. square meter), the volume has this unit to the power of three (e.g. cubic meter). A/V has this unit ^{-1} .

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