Acronym | tetdip |
Name |
tetrahedron-tetrahedron duoprism, vertex figure of he |
Circumradius | sqrt(3)/2 = 0.866025 |
Inradius | 1/sqrt(24) = 0.204124 |
Volume | 1/72 = 0.013889 |
Surface | 1/sqrt(6) = 0.408248 |
Dihedral angles | |
Face vector | 16, 48, 68, 56, 28, 8 |
Confer |
|
External links |
This duoprism can also be seen as segmentopeton, cf. below. That one can be blended (externally) at its larger base with the one with inverted alignment, i.e. with tetal tratet, in order to produce a bistratic stack, which still happens to be orbiform (oxo3ooo oxx3ooo3xoo&#xt).
Incidence matrix according to Dynkin symbol
x3o3o x3o3o . . . . . . | 16 | 3 3 | 3 9 3 | 1 9 9 1 | 3 9 3 | 3 3 ------------+----+-------+----------+-----------+--------+---- x . . . . . | 2 | 24 * | 2 3 0 | 1 6 3 0 | 3 6 1 | 3 2 . . . x . . | 2 | * 24 | 0 3 2 | 0 3 6 1 | 1 6 3 | 2 3 ------------+----+-------+----------+-----------+--------+---- x3o . . . . | 3 | 3 0 | 16 * * | 1 3 0 0 | 3 3 0 | 3 1 x . . x . . | 4 | 2 2 | * 36 * | 0 2 2 0 | 1 4 1 | 2 2 . . . x3o . | 3 | 0 3 | * * 16 | 0 0 3 1 | 0 3 3 | 1 3 ------------+----+-------+----------+-----------+--------+---- x3o3o . . . ♦ 4 | 6 0 | 4 0 0 | 4 * * * | 3 0 0 | 3 0 x3o . x . . ♦ 6 | 6 3 | 2 3 0 | * 24 * * | 1 2 0 | 2 1 x . . x3o . ♦ 6 | 3 6 | 0 3 2 | * * 24 * | 0 2 1 | 1 2 . . . x3o3o ♦ 4 | 0 6 | 0 0 4 | * * * 4 | 0 0 3 | 0 3 ------------+----+-------+----------+-----------+--------+---- x3o3o x . . ♦ 8 | 12 4 | 8 6 0 | 2 4 0 0 | 6 * * | 2 0 x3o . x3o . ♦ 9 | 9 9 | 3 9 3 | 0 3 3 0 | * 16 * | 1 1 x . . x3o3o ♦ 8 | 4 12 | 0 6 8 | 0 0 4 2 | * * 6 | 0 2 ------------+----+-------+----------+-----------+--------+---- x3o3o x3o . ♦ 12 | 18 12 | 12 18 4 | 3 12 6 0 | 3 4 0 | 4 * x3o . x3o3o ♦ 12 | 12 18 | 4 18 12 | 0 6 12 3 | 0 4 3 | * 4
or . . . . . . | 16 | 6 | 6 9 | 2 18 | 6 9 | 6 ---------------+----+----+-------+------+-------+-- x . . . . . & | 2 | 48 | 2 3 | 1 9 | 4 6 | 5 ---------------+----+----+-------+------+-------+-- x3o . . . . & | 3 | 3 | 32 * | 1 3 | 3 3 | 4 x . . x . . | 4 | 4 | * 36 | 0 4 | 2 4 | 4 ---------------+----+----+-------+------+-------+-- x3o3o . . . & ♦ 4 | 6 | 4 0 | 8 * | 3 0 | 3 x3o . x . . & ♦ 6 | 9 | 2 3 | * 48 | 1 2 | 3 ---------------+----+----+-------+------+-------+-- x3o3o x . . & ♦ 8 | 16 | 8 6 | 2 4 | 12 * | 2 x3o . x3o . ♦ 9 | 18 | 6 9 | 0 6 | * 16 | 2 ---------------+----+----+-------+------+-------+-- x3o3o x3o . & ♦ 12 | 30 | 16 18 | 3 18 | 3 4 | 8
ox3oo xx3oo3oo&#x → height = sqrt(2/3) = 0.816497
(tet || tratet)
o.3o. o.3o.3o. | 4 * | 3 3 0 0 | 3 3 9 0 0 0 | 1 1 9 9 0 0 0 | 3 9 3 0 0 | 3 3 0
.o3.o .o3.o3.o | * 12 | 0 1 2 3 | 0 2 3 1 6 3 | 0 1 6 3 3 6 1 | 3 6 1 3 2 | 3 2 1
------------------+------+------------+-----------------+------------------+------------+------
.. .. x. .. .. | 2 0 | 6 * * * | 2 0 3 0 0 0 | 1 0 3 6 0 0 0 | 1 6 3 0 0 | 2 2 0
oo3oo oo3oo3oo&#x | 1 1 | * 12 * * | 0 2 3 0 0 0 | 0 1 6 3 0 0 0 | 3 6 1 0 0 | 3 2 0
.x .. .. .. .. | 0 2 | * * 12 * | 0 1 0 1 3 0 | 0 1 3 0 3 3 0 | 3 3 0 3 1 | 3 1 1
.. .. .x .. .. | 0 2 | * * * 18 | 0 0 1 0 2 2 | 0 0 2 2 1 4 1 | 1 4 1 2 2 | 2 2 1
------------------+------+------------+-----------------+------------------+------------+------
.. .. x.3o. .. | 3 0 | 3 0 0 0 | 4 * * * * * | 1 0 0 3 0 0 0 | 0 3 3 0 0 | 1 3 0
ox .. .. .. ..&#x | 1 2 | 0 2 1 0 | * 12 * * * * | 0 1 3 0 0 0 0 | 3 3 0 0 0 | 3 1 0
.. .. xx .. ..&#x | 2 2 | 1 2 0 1 | * * 18 * * * | 0 0 2 2 0 0 0 | 1 4 1 0 0 | 2 2 0
.x3.o .. .. .. | 0 3 | 0 0 3 0 | * * * 4 * * | 0 1 0 0 3 0 0 | 3 0 0 3 0 | 3 0 1
.x .. .x .. .. | 0 4 | 0 0 2 2 | * * * * 18 * | 0 0 1 0 1 2 0 | 1 2 0 2 1 | 2 1 1
.. .. .x3.o .. | 0 3 | 0 0 0 3 | * * * * * 12 | 0 0 0 1 0 2 1 | 0 2 1 1 2 | 1 2 1
------------------+------+------------+-----------------+------------------+------------+------
.. .. x.3o.3o. ♦ 4 0 | 6 0 0 0 | 4 0 0 0 0 0 | 1 * * * * * * | 0 0 3 0 0 | 0 3 0
ox3oo .. .. ..&#x ♦ 1 3 | 0 3 3 0 | 0 3 0 1 0 0 | * 4 * * * * * | 3 0 0 0 0 | 3 0 0
ox .. xx .. ..&#x ♦ 2 4 | 1 4 2 2 | 0 2 2 0 1 0 | * * 18 * * * * | 1 2 0 0 0 | 2 1 0
.. .. xx3oo ..&#x ♦ 3 3 | 3 3 0 3 | 1 0 3 0 0 1 | * * * 12 * * * | 0 2 1 0 0 | 1 2 0
.x3.o .x .. .. ♦ 0 6 | 0 0 6 3 | 0 0 0 2 3 0 | * * * * 6 * * | 1 0 0 2 0 | 2 0 1
.x .. .x3.o .. ♦ 0 6 | 0 0 3 6 | 0 0 0 0 3 2 | * * * * * 12 * | 0 1 0 1 1 | 1 1 1
.. .. .x3.o3.o ♦ 0 4 | 0 0 0 6 | 0 0 0 0 0 4 | * * * * * * 3 | 0 0 1 0 2 | 0 2 1
------------------+------+------------+-----------------+------------------+------------+------
ox3oo xx .. ..&#x ♦ 2 6 | 1 6 6 3 | 0 6 3 2 3 0 | 0 2 3 0 1 0 0 | 6 * * * * | 2 0 0
ox .. xx3oo ..&#x ♦ 3 6 | 3 6 3 6 | 1 3 6 0 3 2 | 0 0 3 2 0 1 0 | * 12 * * * | 1 1 0
.. .. xx3oo3oo&#x ♦ 4 4 | 6 4 0 6 | 4 0 6 0 0 4 | 1 0 0 4 0 0 1 | * * 3 * * | 0 2 0
.x3.o .x3.o .. ♦ 0 9 | 0 0 9 9 | 0 0 0 3 9 3 | 0 0 0 0 3 3 0 | * * * 4 * | 1 0 1
.x .. .x3.o3.o ♦ 0 8 | 0 0 4 12 | 0 0 0 0 6 8 | 0 0 0 0 0 4 2 | * * * * 3 | 0 1 1
------------------+------+------------+-----------------+------------------+------------+------
ox3oo xx3oo ..&#x ♦ 3 9 | 3 9 9 9 | 1 9 9 3 9 3 | 0 3 9 3 3 3 0 | 3 3 0 1 0 | 4 * *
ox .. xx3oo3oo&#x ♦ 4 8 | 6 8 4 12 | 4 4 12 0 6 8 | 1 0 6 8 0 4 2 | 0 4 2 0 1 | * 3 *
.x3.o .x3.o3.o ♦ 0 12 | 0 0 12 18 | 0 0 0 4 18 12 | 0 0 0 0 6 12 3 | 0 0 0 4 3 | * * 1
xo ox xx3oo3oo&#x → height = 1/sqrt(2) = 0.707107
(tepe || lacing-ortho tepe)
o. o. o.3o.3o. | 8 * | 1 3 2 0 0 | 3 3 2 1 6 0 0 | 3 1 1 6 3 6 0 0 | 1 3 6 3 2 0 | 3 2 1
.o .o .o3.o3.o | * 8 | 0 0 2 1 3 | 0 0 1 2 6 3 3 | 0 0 1 3 6 6 3 1 | 0 3 3 6 2 1 | 3 1 2
------------------+-----+--------------+----------------+--------------------+-------------+------
x. .. .. .. .. | 2 0 | 4 * * * * | 3 0 2 0 0 0 0 | 3 0 1 6 0 0 0 0 | 1 3 6 0 0 0 | 3 2 0
.. .. x. .. .. | 2 0 | * 12 * * * | 1 2 0 0 2 0 0 | 2 1 0 2 1 0 0 0 | 1 1 4 2 2 0 | 2 2 1
oo oo oo3oo3oo&#x | 1 1 | * * 16 * * | 0 0 1 1 3 0 0 | 0 0 1 3 3 3 0 0 | 0 3 3 3 1 0 | 3 1 1
.. .x .. .. .. | 0 2 | * * * 4 * | 0 0 0 2 0 3 0 | 0 0 1 0 6 0 3 0 | 0 3 0 6 0 1 | 3 0 2
.. .. .x .. .. | 0 2 | * * * * 12 | 0 0 0 0 2 1 2 | 0 0 0 1 2 4 2 1 | 0 1 2 4 2 1 | 2 1 2
------------------+-----+--------------+----------------+--------------------+-------------+------
x. .. x. .. .. | 4 0 | 2 2 0 0 0 | 6 * * * * * * | 2 0 0 2 0 0 0 0 | 1 1 4 0 0 0 | 2 2 0
.. .. x.3o. .. | 3 0 | 0 3 0 0 0 | * 8 * * * * * | 1 1 0 0 0 2 0 0 | 1 0 2 1 2 0 | 1 2 1
xo .. .. .. ..&#x | 2 1 | 1 0 2 0 0 | * * 8 * * * * | 0 0 1 3 0 0 0 0 | 0 3 3 0 0 0 | 3 1 0
.. ox .. .. ..&#x | 1 2 | 0 0 2 1 0 | * * * 8 * * * | 0 0 1 0 3 0 0 0 | 0 3 0 3 0 0 | 3 0 1
.. .. xx .. ..&#x | 2 2 | 0 1 2 0 1 | * * * * 24 * * | 0 0 0 1 1 2 0 0 | 0 1 2 2 1 0 | 2 1 1
.. .x .x .. .. | 0 4 | 0 0 0 2 2 | * * * * * 6 * | 0 0 0 0 2 0 2 0 | 0 1 0 4 0 1 | 2 0 2
.. .. .x3.o .. | 0 3 | 0 0 0 0 3 | * * * * * * 8 | 0 0 0 0 0 2 1 1 | 0 0 1 2 2 1 | 1 1 2
------------------+-----+--------------+----------------+--------------------+-------------+------
x. .. x.3o. .. ♦ 6 0 | 3 6 0 0 0 | 3 2 0 0 0 0 0 | 4 * * * * * * * | 1 0 2 0 0 0 | 1 2 0
.. .. x.3o.3o. ♦ 4 0 | 0 6 0 0 0 | 0 4 0 0 0 0 0 | * 2 * * * * * * | 1 0 0 0 2 0 | 0 2 1
xo ox .. .. ..&#x ♦ 2 2 | 1 0 4 1 0 | 0 0 2 2 0 0 0 | * * 4 * * * * * | 0 3 0 0 0 0 | 3 0 0
xo .. xx .. ..&#x ♦ 4 2 | 2 2 4 0 1 | 1 0 2 0 2 0 0 | * * * 12 * * * * | 0 1 2 0 0 0 | 2 1 0
.. ox xx .. ..&#x ♦ 2 4 | 0 1 4 2 2 | 0 0 0 2 2 1 0 | * * * * 12 * * * | 0 1 0 2 0 0 | 2 0 1
.. .. xx3oo ..&#x ♦ 3 3 | 0 3 3 0 3 | 0 1 0 0 3 0 1 | * * * * * 16 * * | 0 0 1 1 1 0 | 1 1 1
.. .x .x3.o .. ♦ 0 6 | 0 0 0 3 6 | 0 0 0 0 0 3 2 | * * * * * * 4 * | 0 0 0 2 0 1 | 1 0 2
.. .. .x3.o3.o ♦ 0 4 | 0 0 0 0 6 | 0 0 0 0 0 0 4 | * * * * * * * 2 | 0 0 0 0 2 1 | 0 1 2
------------------+-----+--------------+----------------+--------------------+-------------+------
x. .. x.3o.3o. ♦ 8 0 | 4 12 0 0 0 | 6 8 0 0 0 0 0 | 4 2 0 0 0 0 0 0 | 1 * * * * * | 0 2 0
xo ox xx .. ..&#x ♦ 4 4 | 2 2 8 2 2 | 1 0 4 4 4 1 0 | 0 0 2 2 2 0 0 0 | * 6 * * * * | 2 0 0
xo .. xx3oo ..&#x ♦ 6 3 | 3 6 6 0 3 | 3 2 3 0 6 0 1 | 1 0 0 3 0 2 0 0 | * * 8 * * * | 1 1 0
.. ox xx3oo ..&#x ♦ 3 6 | 0 3 6 3 6 | 0 1 0 3 6 3 2 | 0 0 0 0 3 2 1 0 | * * * 8 * * | 1 0 1
.. .. xx3oo3oo&#x ♦ 4 4 | 0 6 4 0 6 | 0 4 0 0 6 0 4 | 0 1 0 0 0 4 0 1 | * * * * 4 * | 0 1 1
.. .x .x3.o3.o ♦ 0 8 | 0 0 0 4 12 | 0 0 0 0 0 6 8 | 0 0 0 0 0 0 4 2 | * * * * * 1 | 0 0 1
------------------+-----+--------------+----------------+--------------------+-------------+------
xo ox xx3oo ..&#x ♦ 6 6 | 3 6 12 3 6 | 3 2 6 6 12 3 2 | 1 0 3 6 6 4 1 0 | 0 3 2 2 0 0 | 4 * *
xo .. xx3oo3oo&#x ♦ 8 4 | 4 12 8 0 6 | 6 8 4 0 12 0 4 | 4 2 0 6 0 8 0 1 | 1 0 4 0 2 0 | * 2 *
.. ox xx3oo3oo&#x ♦ 4 8 | 0 6 8 4 12 | 0 4 0 4 12 6 8 | 0 1 0 0 6 8 4 2 | 0 0 0 4 2 1 | * * 2
or o. o. o.3o.3o. & | 16 | 1 3 2 | 3 3 3 6 | 3 1 1 9 6 | 1 3 9 2 | 3 3 --------------------+----+---------+-------------+-------------+----------+---- x. .. .. .. .. & | 2 | 8 * * | 3 0 2 0 | 3 0 1 6 0 | 1 3 6 0 | 3 2 .. .. x. .. .. & | 2 | * 24 * | 1 2 0 2 | 2 1 0 3 4 | 1 1 6 2 | 2 3 oo oo oo3oo3oo&#x | 2 | * * 16 | 0 0 2 3 | 0 0 1 6 3 | 0 3 6 1 | 3 2 --------------------+----+---------+-------------+-------------+----------+---- x. .. x. .. .. & | 4 | 2 2 0 | 12 * * * | 2 0 0 2 0 | 1 1 4 0 | 2 2 .. .. x.3o. .. & | 3 | 0 3 0 | * 16 * * | 1 1 0 0 2 | 1 0 3 2 | 1 3 xo .. .. .. ..&#x & | 3 | 1 0 2 | * * 16 * | 0 0 1 3 0 | 0 3 3 0 | 3 1 .. .. xx .. ..&#x | 4 | 0 2 2 | * * * 24 | 0 0 0 2 2 | 0 1 4 1 | 2 2 --------------------+----+---------+-------------+-------------+----------+---- x. .. x.3o. .. & ♦ 6 | 3 6 0 | 3 2 0 0 | 8 * * * * | 1 0 2 0 | 1 2 .. .. x.3o.3o. & ♦ 4 | 0 6 0 | 0 4 0 0 | * 4 * * * | 1 0 0 2 | 0 3 xo ox .. .. ..&#x ♦ 4 | 2 0 4 | 0 0 4 0 | * * 4 * * | 0 3 0 0 | 3 0 xo .. xx .. ..&#x & ♦ 6 | 2 3 4 | 1 0 2 2 | * * * 24 * | 0 1 2 0 | 2 1 .. .. xx3oo ..&#x ♦ 6 | 0 6 3 | 0 2 0 3 | * * * * 16 | 0 0 2 1 | 1 2 --------------------+----+---------+-------------+-------------+----------+---- x. .. x.3o.3o. & ♦ 8 | 4 12 0 | 6 8 0 0 | 4 2 0 0 0 | 2 * * * | 2 0 xo ox xx .. ..&#x ♦ 8 | 4 4 8 | 2 0 8 4 | 0 0 2 4 0 | * 6 * * | 2 0 xo .. xx3oo ..&#x & ♦ 9 | 3 9 6 | 3 3 3 6 | 1 0 0 3 2 | * * 16 * | 1 1 .. .. xx3oo3oo&#x ♦ 8 | 0 12 4 | 0 8 0 6 | 0 2 0 0 4 | * * * 4 | 0 2 --------------------+----+---------+-------------+-------------+----------+---- xo ox xx3oo ..&#x ♦ 12 | 6 12 12 | 6 4 12 12 | 2 0 3 12 4 | 0 3 4 0 | 4 * xo .. xx3oo3oo&#x & ♦ 12 | 4 18 8 | 6 12 4 12 | 4 3 0 6 8 | 1 0 4 2 | * 4
© 2004-2024 | top of page |