1D Line , Circular Arc , Parabola , Helix , Koch Curve
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 , 1/2 EL Triangle , Quadrilateral , Rectangle , Golden Rectangle , Rhombus , Parallelogram , Kite , 60-90-120 Kite , Half Square Kite , Right Kite , Trapezoid , Right Trapezoid , Isosceles Trapezoid , Tri-equilateral Trapezoid , Obtuse Trapezoid , Cyclic Quadrilateral , Tangential Quadrilateral , Arrowhead , Concave Quadrilateral , Crossed Rectangle , Antiparallelogram , House-Shape , Symmetric Pentagon , Diagonally Bisected Octagon , Cut Rectangle , Concave Pentagon , Concave Regular Pentagon , Stretched Pentagon , Straight Bisected Octagon , Stretched Hexagon , Symmetric Hexagon , Semi-regular Hexagon , Parallelogon , Concave Hexagon , Arrow-Hexagon , Rectangular Hexagon , L-Shape , Sharp Kink , T-Shape , Square Heptagon , Truncated Square , Stretched Octagon , Frame , Open Frame , Grid , Cross , X-Shape , H-Shape , Threestar , Fourstar , Pentagram , Hexagram , Unicursal Hexagram , Oktagram , Star of Lakshmi , Double Star Polygon , Polygram , The Hat , Polygon
Round Forms: Circle , Semicircle , Circular Sector , Circular Segment , Circular Layer , Circular Central Segment , Round Corner , Circular Corner , Circle Tangent Arrow , Drop Shape , Crescent , Pointed Oval , Two Circles , Lancet Arch , Knoll , Annulus , Semi-Annulus , Annulus Sector , Annulus Segment , Cash , Curved Rectangle , Rounded Polygon , Rounded Rectangle , Ellipse , Semi-Ellipse , Elliptical Segment , Elliptical Sector , Elliptical Ring , Stadium , Spiral , Log. Spiral , Reuleaux Triangle , Cycloid , Double Cycloid , Astroid , Hypocycloid , Cardioid , Epicycloid , Parabolic Segment , Heart , Tricorn , Pointed Semicircle , Interarc Triangle , Circular Arc Triangle , Interarc Quadrangle , Intercircle Quadrangle , Circular Arc Quadrangle , Circular Arc Polygon , Claw , Half Yin-Yang , Arbelos , Salinon , Bulge , Lune , Three Circles , Polycircle , Round-Edged Polygon , Rose , Gear , Oval , Egg-Profile , Lemniscate , Squircle , Circular Square , Digon , Spherical Triangle
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 , Rhombicosidodecahedron , Truncated Icosidodecahedron , Snub Dodecahedron
Catalan Solids: Triakis Tetrahedron , Rhombic Dodecahedron , Triakis Octahedron , Tetrakis Hexahedron , Deltoidal Icositetrahedron , Hexakis Octahedron , Rhombic Triacontahedron , Triakis Icosahedron , Pentakis Dodecahedron , Pentagonal Icositetrahedron , Deltoidal Hexecontahedron , Hexakis Icosahedron , Pentagonal Hexecontahedron
Johnson Solids: Pyramids , Cupolae , Rotunda , Elongated Pyramids , Gyroelongated Pyramids , Bipyramids , Elongated Bipyramids , Gyroelongated Square Dipyramid , Gyrobifastigium , Disheptahedron , Snub Disphenoid , Sphenocorona , Disphenocingulum
Other Polyhedrons: Cuboid , Square Pillar , Triangular Pyramid , Square Pyramid , Regular Pyramid , Pyramid , Square Frustum , Regular Frustum , Frustum , Bent Pyramid , Regular Bipyramid , Bipyramid , Bifrustum , Frustum-Pyramid , Ramp , Right Wedge , Wedge , Half Tetrahedron , Rhombohedron , Parallelepiped , Regular Prism , Prism , Oblique Prism , Anticube , Antiprism , Prismatoid , Trapezohedron , Disphenoid , Corner , General Tetrahedron , Wedge-Cuboid , Half Cuboid , Skewed Cuboid , Ingot , Skewed Three-Edged Prism , Cut Cuboid , Truncated Cuboid , Obtuse Edged Cuboid , Elongated Dodecahedron , Truncated Rhombohedron , Obelisk , Bent Cuboid , Hollow Cuboid , Hollow Pyramid , Hollow Frustum , Star Pyramid , Stellated Octahedron , Small Stellated Dodecahedron , Great Stellated Dodecahedron , Great Dodecahedron , Great Icosahedron
Round Forms: Sphere , Hemisphere , Spherical Corner , Cylinder , Cut Cylinder , Oblique Cylinder , Bent Cylinder , Elliptic Cylinder , Generalized Cylinder , Cone , Truncated Cone , Oblique Circular Cone , Elliptic Cone , Truncated Elliptic Cone , General Cone , General Truncated Cone , Bicone , Truncated Bicone , Pointed Pillar , Rounded Cone , Drop , Spheroid , Ellipsoid , Semi-Ellipsoid , Spherical Sector , Spherical Cap , Spherical Segment , Spherical Central Segment , Double Calotte , Double Sphere , Spherical Wedge , Half Cylinder , Diagonally Halved Cylinder , Cylindrical Wedge , Cylindrical Sector , Cylindrical Segment , Flat End Cylinder , Half Cone , Conical Sector , Conical Wedge , Spherical Shell , Half Spherical Shell , Spherical Shell Cap , Cylindrical Shell , Cut Cylindrical Shell , Oblique Cylindrical Shell , Hollow Cone , Truncated Hollow Cone , Spherical Ring , Torus , Spindle Torus , Toroid , Torus Sector , Toroid Sector , Arch , Reuleaux-Tetrahedron , Capsule , Capsule Segment , Double Point , Anticone , Truncated Anticone , Sphere-Cylinder , Lens , Concave Lens , Barrel , Egg Shape , Paraboloid , Hyperboloid , Oloid , Steinmetz Solids , Solid of Revolution
4D
Tesseract , Hypersphere
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The Hat
Calculations at the geometric figure The Hat, which was discovered in 2022 by the English amateur mathematician David Smith and which is a solution to the Einstein problem. This has nothing to do with Albert Einstein, but is a pun with the German ein Stein (one stone). With this shape, a plane can be tiled without gaps without creating a recurring pattern. It was the first such form to be discovered. The Hat is made of eight equal 60-90-120-90 deltoids and has 13 sides and vertices. Enter one value and choose the number of decimal places. Then click Calculate.

Formulas:
b = √3 a
w = 6 a
h = 2,5 * √3 * a
p = 8 a + 6 b = ( 8 + 6√3 ) a
A = 8 √3 a²

Lengths, width, height and perimeter have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).

Surfaces tiled with The Hat tile consist of these tiles, which lie next to one another and can be rotated and mirrored. A modification of The Hat, discovered shortly afterwards, in which the straight edges are replaced by special curves, produces a similar family of tiles. With each tile from this family, the surface can be tiled even without mirroring, without creating a regular pattern. This shape is called Spectre, it meets even stricter conditions of the Einstein problem. Due to the irregular curvature of these tiles, calculating their perimeter and area is very complicated.
Tiles that represent a solution to the Einstein problem are sometimes referred to directly as einstein , written in lowercase.

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