Bixylodiminished hydrochoron (EntityTopic, 13)

From Hi.gher. Space

(Difference between revisions)

Revision as of 18:50, 24 August 2012

The bixylodiminished hydrochoron, abbreviated BXD, is a CRF polychoron obtained by removing the vertices of two of the five inscribed xylochora from a hydrochoron. Removing the vertices of only one yields the snub demitesseract, which can therefore also be called the (mono) xylodiminished hydrochoron. Like the snub demitesseract, it exists in two chiral forms. Surprisingly, although the resulting polychoron is not uniform, it is both cell- and vertex-transitive; its 48 cells are tridiminished icosahedra. This cell transitivity gives it a much simpler FLD, with only four nodes, than the vast majority of other CRF polychora and even many uniform polychora.

While the tridiminished icosahedron has four types of edges (top to pen, pen to pen, pen to lat, lat to bot), the BXD has only two types: pen-3-lat, which has four cells around each instance, separated by three pentagons and one lateral, and the top-pen-lat-top loop, which has three cells around each instance and includes the other laterals. Note that the six pen-to-lat edges are divided into two groups of three due to the chirality of the BXD, the first group ending as pen-3-lats, the second ending up as loops. From this information and the fact that it has 48 cells, we can work out that there are 6×48÷4 = 72 edges of the pen-3-lat type and 9×48÷3 = 144 edges of the loop type.

External links

Structure of the bixylodiminished hydrochoron explained at Eusebeia

Notable Tetrashapes
Regular:	pyrochoron • aerochoron • geochoron • xylochoron • hydrochoron • cosmochoron
Powertopes:	triangular octagoltriate • square octagoltriate • hexagonal octagoltriate • octagonal octagoltriate
Circular:	glome • cubinder • duocylinder • spherinder • sphone • cylindrone • dicone • coninder
Torii:	tiger • torisphere • spheritorus • torinder • ditorus

@@ Line 1: / Line 1: @@
 {{STS Shape
 | dim=4
-| elements=48, 192, 228, 72
+| elements=48, 192, 216, 72
 | extra={{STS Polytope
 | flayout={{FLD2|dim=4|a3bvert|sp01}}{{FLD2|dim=4|a3tvert|sp02}}
 }}}}
-The '''bixylodiminished hydrochoron''' is a [[CRF polychoron]] obtained by removing the vertices of two of the five inscribed [[xylochora]] from a [[hydrochoron]]. Removing the vertices of only one yields the [[snub demitesseract]], which can therefore also be called the (mono) ''xylodiminished hydrochoron''. Like the snub demitesseract, it exists in two chiral forms. Surprisingly, although the resulting polychoron is not [[uniform]], it is both cell- and vertex-transitive; its 48 cells are [[tridiminished icosahedra]]. This cell transitivity gives it a much simpler [[FLD]], with only four nodes, than the vast majority of other CRF polychora and even many uniform polychora.
+The '''bixylodiminished hydrochoron''', abbreviated '''BXD''', is a [[CRF polychoron]] obtained by removing the vertices of two of the five inscribed [[xylochora]] from a [[hydrochoron]]. Removing the vertices of only one yields the [[snub demitesseract]], which can therefore also be called the (mono) ''xylodiminished hydrochoron''. Like the snub demitesseract, it exists in two chiral forms. Surprisingly, although the resulting polychoron is not [[uniform]], it is both cell- and vertex-transitive; its 48 cells are [[tridiminished icosahedra]]. This cell transitivity gives it a much simpler [[FLD]], with only four nodes, than the vast majority of other CRF polychora and even many uniform polychora.
-While the tridiminished icosahedron has four types of edges (top to pen, pen to pen, pen to lat, lat to bot), the bixylodiminished hydrochoron has only two types: ''pen to pen'', which has four cells around each instance, and the ''top-pen-lat-top loop'', which has three cells around each instance. From this information and the fact that it has 48 cells, we can work out that there are 3×48÷4 = 36 edges of the pen to pen type and 12×48÷3 = 192 edges of the loop type.
+While the tridiminished icosahedron has four types of edges (top to pen, pen to pen, pen to lat, lat to bot), the BXD has only two types: ''pen-3-lat'', which has four cells around each instance, separated by three pentagons and one lateral, and the ''top-pen-lat-top loop'', which has three cells around each instance and includes the other laterals. Note that the six pen-to-lat edges are divided into two groups of three due to the chirality of the BXD, the first group ending as pen-3-lats, the second ending up as loops. From this information and the fact that it has 48 cells, we can work out that there are 6×48÷4 = 72 edges of the pen-3-lat type and 9×48÷3 = 144 edges of the loop type.
 == External links ==