Aale de Winkel wrote:the qualitative descriptions of the 4d hypercylinders are a bit foggy:
hypercylinder: (x[sub]k[/sub]: x[sub]k[/sub] x[sup]k[/sup] = r[sup]2[/sup]; k = 1,2; other for k > 2)
2d: same as circle
3d cylinder: x[sup]2[/sup] + y[sup]2[/sup] = r[sup]2[/sup], z = 0 .. dz
4d cubinder: x[sup]2[/sup] + y[sup]2[/sup] = r[sup]2[/sup], z = 0 .. dz, w = 0 .. dw
4d duocylinder: x[sup]2[/sup] + y[sup]2[/sup] = r[sup]2[/sup], z[sup]2[/sup] + w[sup]2[/sup] = r[sup]2[/sup]
4d spherinder: x[sup]2[/sup] + y[sup]2[/sup] + z[sup]2[/sup] = r[sup]2[/sup], w = 0 .. dw
bobxp wrote:A hypercylinder is a n-d solid with one hyperspherical face.
cubone
Aale de Winkel wrote:hypercylinder: (x[sub]k[/sub]: x[sub]k[/sub] x[sup]k[/sup] = r[sup]2[/sup]; k = 1..l; linear for k > l; l < n)
hypercone: (x[sub]k[/sub]: x[sub]k[/sub] x[sup]k[/sup] = x[sub]l[/sub][sup]2[/sup]; k = 1..l-1; linear for k >= l; l <= n)
bobxp wrote:And I have made a term for a 4 dimensional pyramid: the hyperpyramid (ie, a sphere-based hyperpyramid for example)
bobxp wrote:You can even base hyperpyramids off of pyramids, eg:
a "square based pyramidal hyperpyramid" - a "square" is conically extruded to form a "square based pyramid", which is then conically extruded to form a "square based pyramidal hyperpyramid".
You can also do this with other things, eg:
a "hexagonal prismidal hyperpyramid" - a "hexagon" is linearly extruded to form a "hexagonal prism", which is then conically extruded to form a "hexagonal prismidal hyperpyramid".
bobxp wrote:I just realised I've made quite a few shape-developing terms:
lathing
conical extrusion
linear extrusion
alkaline wrote:bobxp wrote:And I have made a term for a 4 dimensional pyramid: the hyperpyramid (ie, a sphere-based hyperpyramid for example)
I was talking specifically about the square based one. The problem with the hyper prefix is that depending on its context, it usually means either 4+ dimensions or n dimensions, and it doesn't mean only =4 dimensions very often.
bobxp wrote:You can even base hyperpyramids off of pyramids, eg:
a "square based pyramidal hyperpyramid" - a "square" is conically extruded to form a "square based pyramid", which is then conically extruded to form a "square based pyramidal hyperpyramid".
You can also do this with other things, eg:
a "hexagonal prismidal hyperpyramid" - a "hexagon" is linearly extruded to form a "hexagonal prism", which is then conically extruded to form a "hexagonal prismidal hyperpyramid".
These giant compounds become unwieldy very quickly. That's why we've used the practice of "blend" compounds.
bobxp wrote:I just realised I've made quite a few shape-developing terms:
lathing
conical extrusion
linear extrusion
here are some fun word suggestions:
contrude = con(icly ex)trude
lintrude = lin(early ex)trude
bobxp wrote:cubone
And I have made a term for a 4 dimensional pyramid: the hyperpyramid (ie, a sphere-based hyperpyramid for example)
You can even base hyperpyramids off of pyramids, eg:
a "square based pyramidal hyperpyramid" - a "square" is conically extruded to form a "square based pyramid", which is then conically extruded to form a "square based pyramidal hyperpyramid".
You can also do this with other things, eg:
a "hexagonal prismidal hyperpyramid" - a "hexagon" is linearly extruded to form a "hexagonal prism", which is then conically extruded to form a "hexagonal prismidal hyperpyramid".
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