Acronym diddoh
Name hyperbolic disdodecahedral honeycomb,
hyperbolic bitruncated order 5 dodecahedral honeycomb
 
 ©
Circumradius sqrt[-1-sqrt(5)] = 1.798907 i
Vertex figure
 ©
Confer
contained pseudo cells:
x6o4o  
general polytopal classes:
noble polytopes  
External
links
wikipedia   polytopewiki  

As can be read from the matrices below, at every edge there are 2 hexagons. Thus we get as pseudo cells something with hexagons only. From the vertex incidence we further read off that this pseudo tiling happens to use 4 hexagons per vertex. From the here truely being used cells (ti) it is deduced, that any straight edge sequence of that seeming x6o4o needs to be mod-wrapped to pentagonal holes. Therefore those pseudo cells rather are the skew polyhedron x6o4o|5 instead.


Incidence matrix according to Dynkin symbol

o5x3x5o   (N → ∞)

. . . . | 30N |   2   2 |  1   4  1 | 2 2
--------+-----+---------+-----------+----
. x . . |   2 | 30N   * |  1   2  0 | 2 1
. . x . |   2 |   * 30N |  0   2  1 | 1 2
--------+-----+---------+-----------+----
o5x . . |   5 |   5   0 | 6N   *  * | 2 0
. x3x . |   6 |   3   3 |  * 20N  * | 1 1
. . x5o |   5 |   0   5 |  *   * 6N | 0 2
--------+-----+---------+-----------+----
o5x3x .   60 |  60  30 | 12  20  0 | N *
. x3x5o   60 |  30  60 |  0  20 12 | * N
or
. . . .    | 15N |   4 |  2   4 | 4
-----------+-----+-----+--------+--
. x . .  & |   2 | 30N |  1   2 | 3
-----------+-----+-----+--------+--
o5x . .  & |   5 |   5 | 6N   * | 2
. x3x .    |   6 |   6 |  * 10N | 2
-----------+-----+-----+--------+--
o5x3x .  &   60 |  90 | 12  20 | N

© 2004-2024
top of page