Bixylodiminished hydrochoron (EntityTopic, 13)

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The '''bixylodiminished hydrochoron''' is a [[CRF polychoron]] obtained by removing the vertices of two 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.
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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.
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 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.

Revision as of 23:03, 21 August 2012


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.

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.

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Notable Tetrashapes
Regular: pyrochoronaerochorongeochoronxylochoronhydrochoroncosmochoron
Powertopes: triangular octagoltriatesquare octagoltriatehexagonal octagoltriateoctagonal octagoltriate
Circular: glomecubinderduocylinderspherindersphonecylindronediconeconinder
Torii: tigertorispherespheritorustorinderditorus