Search results

...ck-S-Woods-Plane/bams/1183414982.full Review of ''Plane and Solid Analytic geometry''] via [[Project Euclid]]</ref> ...[[curvature of Riemannian manifolds]]. In 1903 he spoke on [[non-Euclidean geometry]]. ...

{{legend-line|solid #4169E1|Reference triangle {{math|△''ABC''}}}} {{legend-line|solid #222222|Circumcircle of {{math|△''ABC''}}}} ...

|bgcolor=#e7dcc3|4-face type||[[Runcinated tesseract]][[File:Schlegel half-solid runcinated 8-cell.png|40px]]<BR> [[Truncated tesseract]] [[File:Schlegel half-solid truncated tesseract.png|40px]]<BR> ...

[[File:Steinmetz-cc.svg|300px|thumb|Steinmetz solid (intersection of two cylinders) involving Steinmetz curves (purple)]] ...se of <math> a=b</math> the Steimetz curves are the edges of a [[Steinmetz solid]]. If the cylinder axes are the x- and y-axes and <math>a\le b</math>, then ...

{{Short description|Shape in Euclidean geometry}} [[bitruncated 16-cell|2t{3,3,4}]] [[File:Schlegel half-solid bitruncated 16-cell.png|40px]]<BR> ...

|bgcolor=#e7dcc3|4-face type||[[bitruncated tesseract]] [[File:Schlegel half-solid bitruncated 16-cell.png|40px]]<BR> [[runcitruncated 16-cell]] [[File:Schlegel half-solid runcitruncated 16-cell.png|40px]] ...

...24-cell.png|40px]]<BR>[[Truncated 16-cell|t{3,3,4}]] [[File:Schlegel half-solid truncated 16-cell.png|40px]] ...space. It is constructed by [[24-cell]] and [[truncated 16-cell]] [[Facet (geometry)|facets]]. ...

...a4d.png|40px]]<BR>[[bitruncated tesseract|2t{4,3,3}]] [[File:Schlegel half-solid bitruncated 16-cell.png|40px]]<BR>[[truncated tetrahedral prism|t{3,3}×{}]] ...space-filling [[tessellation]] (or [[honeycomb (geometry)|honeycomb]]) in Euclidean 4-space. ...

{{Short description|Uniform space-filling tessellation in Euclidean 4-space}} ...0px]]<BR>[[truncated 16-cell|t_0,1{3,3,4}]] [[File:Schlegel half-solid truncated 16-cell.png|40px]]<BR>[[octahedral prism|{3,4}×{}]] [[File:Octahe ...

|bgcolor=#e7dcc3|4-face type||[[Truncated 24-cell]] [[File:Schlegel half-solid truncated 24-cell.png|40px]]<BR> [[Omnitruncated tesseract]] [[File:Schlegel half-solid omnitruncated 8-cell.png|40px]] ...

==In ordered structures and Euclidean spaces== ...language=en}}</ref> [[Half-space (geometry)|Half-space]]s and [[Half-line (geometry)|half-lines]] are sometimes described as semi-infinite regions. ...

|bgcolor=#e7dcc3|4-face type||[[truncated tesseract]] [[File:Schlegel half-solid truncated tesseract.png|40px]]<BR>[[16-cell]] [[File:Schlegel wireframe 16- ...y)|honeycomb]]) in Euclidean 4-space. It is constructed by a [[Truncation (geometry)|truncation]] of a [[tesseractic honeycomb]] creating [[truncated tesseract ...

...|40px]]<BR>[[rectified 24-cell|t₁{3,4,3}]] [[File:Schlegel half-solid cantellated 16-cell.png|40px]]<BR>[[cuboctahedral prism|t₁{3,4}× ...space-filling [[tessellation]] (or [[honeycomb (geometry)|honeycomb]]) in Euclidean 4-space. ...

== In Euclidean space == If the space being packed is infinite in measure, such as [[Euclidean space]], it is customary to define the density as the limit of densities ex ...

|bgcolor=#e7dcc3|4-face type||[[runcinated tesseract]] [[File:Schlegel half-solid runcinated 8-cell.png|40px]] <BR>[[tesseract]] [[File:Schlegel wireframe 8- ...)|honeycomb]]) in Euclidean 4-space. It is constructed by a [[Runcination (geometry)|runcination]] of a [[tesseractic honeycomb]] creating [[runcinated tessera ...

...ype||[[Cantellated tesseract|t_0,2{4,3,3}]] [[File:Schlegel half-solid cantellated 8-cell.png|40px]]<BR>[[24-cell|t₁{3,3,4}]] [[File:Sc ...|honeycomb]]) in Euclidean 4-space. It is constructed by a [[Cantellation (geometry)|cantellation]] of a [[tesseractic honeycomb]] creating [[cantellated tesse ...

...eframe 8-cell.png|40px]]<BR>[[Cantellated tesseract]] [[File:Schlegel half-solid cantellated 8-cell.png|40px]]<BR>[[Rhombicuboctahedral prism]] [[File:Rhomb ...ntellated tesseractic honeycomb''' is a uniform space-filling [[honeycomb (geometry)|honeycomb]]. ...

...ler characteristic|Euler relation]] on the number of d-dimensional [[Face (geometry)|faces]]. ...math>, and [[Hyperbolic geometry|hyperbolic]], <math>\epsilon = -1</math>, geometry) the relation gains a volume term, but only if the dimension ''n'' is even: ...

...truncated 16-cell.png|40px]]<BR>[[Truncated 16-cell]] [[File:Schlegel half-solid truncated 16-cell.png|40px]] ...space-filling [[tessellation]] (or [[honeycomb (geometry)|honeycomb]]) in Euclidean 4-space. It is constructed by a [[bitruncation]] of a [[tesseractic honeyco ...

...4cell1.png|40px]]<BR>[[rectified tesseract|r{3,4,3}]] [[File:Schlegel half-solid rectified 8-cell.png|40px]]<BR>[[tetrahedral prism|{3,3}×{}]] [[File:Tetrah ...ng [[honeycomb (geometry)|honeycomb]]. It can be seen as a [[Cantellation (geometry)|cantellation]] of the regular [[24-cell honeycomb]], containing [[rectifie ...