Acronym | ... |
Name |
f x3o3o, variation of tetrahedron prism, vertex figure of rectified hyperbolic hecatonicosachoric honeycomb |
Circumradius | sqrt[(6+sqrt(5))/8] = 1.014647 |
Face vector | 8, 16, 14, 6 |
Confer |
using edge sizes x = 1 and f = (1+sqrt(5)/2 = 1.618034
Incidence matrix according to Dynkin symbol
f x3o3o . . . . | 8 | 1 3 | 3 3 | 3 1 --------+---+------+-----+---- f . . . | 2 | 4 * | 3 0 | 3 0 . x . . | 2 | * 12 | 1 2 | 2 1 --------+---+------+-----+---- f x . . | 4 | 2 2 | 6 * | 2 0 . x3o . | 3 | 0 3 | * 8 | 1 1 --------+---+------+-----+---- f x3o . ♦ 6 | 3 6 | 3 2 | 4 * . x3o3o ♦ 4 | 0 6 | 0 4 | * 2
xx3oo3oo&#f → height = (1+sqrt(5)/2 = 1.618034 (tet || tet) o.3o.3o. | 4 * | 3 1 0 | 3 3 0 | 1 3 0 .o3.o3.o | * 4 | 0 1 3 | 0 3 3 | 0 3 1 ------------+-----+-------+-------+------ x. .. .. | 2 0 | 6 * * | 2 1 0 | 1 2 0 oo3oo3oo&#f | 1 1 | * 4 * | 0 3 0 | 0 3 0 .x .. .. | 0 2 | * * 6 | 0 1 2 | 0 2 1 ------------+-----+-------+-------+------ x.3o. .. | 3 0 | 3 0 0 | 4 * * | 1 1 0 xx .. ..&#f | 2 2 | 1 2 1 | * 6 * | 0 2 0 .x3.o .. | 0 3 | 0 0 3 | * * 4 | 0 1 1 ------------+-----+-------+-------+------ x.3o.3o. ♦ 4 0 | 6 0 0 | 4 0 0 | 1 * * xx3oo ..&#f ♦ 3 3 | 3 3 3 | 1 3 1 | * 4 * .x3.o3.o ♦ 0 4 | 0 0 6 | 0 0 4 | * * 1
ff ox3oo&#x → height = sqrt(2/3) = 0.816497 (f-line || f x3o) o. o.3o. | 2 * | 1 3 0 0 | 3 3 0 0 | 3 1 0 .o .o3.o | * 6 | 0 1 1 2 | 1 2 2 1 | 2 1 1 ------------+-----+---------+---------+------ f. .. .. | 2 0 | 1 * * * | 3 0 0 0 | 3 0 0 oo oo3oo&#x | 1 1 | * 6 * * | 1 2 0 0 | 2 1 0 .f .. .. | 0 2 | * * 3 * | 1 0 2 0 | 2 0 1 .. .x .. | 0 2 | * * * 6 | 0 1 1 1 | 1 1 1 ------------+-----+---------+---------+------ ff .. ..&#x | 2 2 | 1 2 1 0 | 3 * * * | 2 0 0 .. ox ..&#x | 1 2 | 0 2 0 1 | * 6 * * | 1 1 0 .f .x .. | 0 4 | 0 0 2 2 | * * 3 * | 1 0 1 .. .x3.o | 0 3 | 0 0 0 3 | * * * 2 | 0 1 1 ------------+-----+---------+---------+------ ff ox ..&#x ♦ 2 4 | 1 4 2 2 | 2 2 1 0 | 3 * * .. ox3oo&#x ♦ 1 3 | 0 3 0 3 | 0 3 0 1 | * 2 * .f .x3.o ♦ 0 6 | 0 0 3 6 | 0 0 3 2 | * * 1
ff xo ox&#x → height = 1/sqrt(2) = 0.707107 ((f,x)-{4} || ortho (f,x)-{4}) o. o. o. | 4 * | 1 1 2 0 0 | 1 2 2 1 0 | 2 1 1 .o .o .o | * 4 | 0 0 2 1 1 | 0 2 1 2 1 | 1 2 1 ------------+-----+-----------+-----------+------ f. .. .. | 2 0 | 2 * * * * | 1 2 0 0 0 | 2 1 0 .. x. .. | 2 0 | * 2 * * * | 1 0 2 0 0 | 2 0 1 oo oo oo&#x | 1 1 | * * 8 * * | 0 1 1 1 0 | 1 1 1 .f .. .. | 0 2 | * * * 2 * | 0 2 0 0 1 | 1 2 0 .. .. .x | 0 2 | * * * * 2 | 0 0 0 2 1 | 0 2 1 ------------+-----+-----------+-----------+------ f. x. .. | 4 0 | 2 2 0 0 0 | 1 * * * * | 2 0 0 ff .. ..&#x | 2 2 | 1 0 2 1 0 | * 4 * * * | 1 1 0 .. xo ..&#x | 2 1 | 0 1 2 0 0 | * * 4 * * | 1 0 1 .. .. ox&#x | 1 2 | 0 0 2 0 1 | * * * 4 * | 0 1 1 .f .. .x | 0 4 | 0 0 0 2 2 | * * * * 1 | 0 2 0 ------------+-----+-----------+-----------+------ ff xo ..&#x ♦ 4 2 | 2 2 4 1 0 | 1 2 2 0 0 | 2 * * ff .. ox&#x ♦ 2 4 | 1 0 4 2 2 | 0 2 0 2 1 | * 2 * .. xo ox&#x ♦ 2 2 | 0 1 4 0 1 | 0 0 2 2 0 | * * 2
or o. o. o. & | 8 | 1 1 1 | 1 2 3 | 3 1 --------------+---+-------+-------+---- f. .. .. & | 2 | 4 * * | 1 2 0 | 3 0 .. x. .. & | 2 | * 4 * | 1 0 2 | 2 1 oo oo oo&#x | 2 | * * 8 | 0 1 2 | 2 1 --------------+---+-------+-------+---- f. x. .. & | 4 | 2 2 0 | 2 * * | 2 0 ff .. ..&#x | 4 | 2 0 2 | * 4 * | 2 0 .. xo ..&#x & | 3 | 0 1 2 | * * 8 | 1 1 --------------+---+-------+-------+---- ff xo ..&#x & ♦ 6 | 3 2 4 | 1 2 2 | 4 * .. xo ox&#x ♦ 4 | 0 2 4 | 0 0 4 | * 2
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