hypercubes
Cubes with extra dimensions
Hypercubes are geometric figures that extend the concept of a cube into four or more dimensions.
A cube is three-dimensional; a hypercube (also called a tesseract in four dimensions) adds another axis perpendicular to all three.
Though impossible to visualize directly, hypercubes appear in mathematics, physics, and computer science: The data structure uses a hypercube topology.
Four-dimensional cubic solid
- verticesCorner points of shapes
- edgesOuter limits or boundaries
- facesFront of heads
- cellsBasic biological units
four-dimensional · projection · cross-section · net · unfolding · rotation · symmetry · octahedron
Something that extends outward
- shadowLight blocked by object
- perspectiveAttitude or spatial rendering
- rotationTurning on an axis
- animationTechnique creating movement illusion
rendering · slice · cross-section · wireframe · stereo · 3D model · interactive · simulation
Many and various
- boundaryLine marking a limit
- embeddingPlacing within surrounding mass
- compactnessState of being compressed
- connectednessState of being linked
metric · fiber · covering · surface · neighborhood · continuous · mapping · deformation
Two-dimensional fictional world
- InterstellarBetween stellar bodies
- fourth dimensionTemporal coordinate in spacetime
- sci-fiFuturistic fiction, abbreviated
- thought experimentHypothetical scenario for reasoning
Carl Sagan · Madeleine L'Engle · mind-bending · counterintuitive · perception · abstraction
Having arbitrary spatial axes
- CartesianOf x-y coordinate geometry
- vectorQuantity with direction
- matrixOrdered numerical arrangement
- linear algebraMathematics of vector spaces
coordinate system · Euclidean · analytic · algebraic · tensor · basis · orthonormal · transformation
tesseract
Four-dimensional cubic solid
cells · four-dimensional · projection · cross-section · net · unfolding · rotation · symmetry · octahedron · orthogonal
projection
Something that extends outward
- shadowLight blocked by object
- perspectiveAttitude or spatial rendering
- rotationTurning on an axis
animation · rendering · slice · cross-section · wireframe · stereo · 3D model · interactive · simulation · Flatland
manifold
Many and various
- boundaryLine marking a limit
- embeddingPlacing within surrounding mass
- compactnessState of being compressed
connectedness · metric · fiber · covering · surface · neighborhood · continuous · mapping · deformation · invariant
Flatland
Two-dimensional fictional world
- InterstellarBetween stellar bodies
- fourth dimensionTemporal coordinate in spacetime
- sci-fiFuturistic fiction, abbreviated
Carl Sagan · Madeleine L'Engle · thought experiment · mind-bending · counterintuitive · perception · abstraction
n-dimensional
Having arbitrary spatial axes
linear algebra · coordinate system · Euclidean · analytic · algebraic · tensor · basis · orthonormal · transformation · binary
hypercubespoints
Units of tally
dots · vertices · singularities · blobs · line segments