octatepe

Acronym	octatepe (alt.: tettet octtric)
Name	oct atop tepe, diminished rix, (tet,tet,oct)-trigonic
Circumradius	sqrt(2/3) = 0.816497
Lace city in approx. ASCII-art	o where: o = o3x3o (oct) t t t = x3o3o (tet)
Coordinates	(1/sqrt(2), 0, 0, 0, sqrt(3/8)) & all permutations and all changes of sign in first 3 coordinates (top base, tet) (1/sqrt(8), 1/sqrt(8), -1/sqrt(8), 1/2, 0) & all even changes of sign in first 3 coordinates resp. change of sign in 4th (bottom base, tepe) coordinates are centered to the bottom base
Confer	uniform relative: rix general polytopal classes: segmentotera lace simplices

Incidence matrix according to Dynkin symbol

ox ox3xo3oo&#x   → height = sqrt(3/8) = 0.612372
(oct || tepe)

o. o.3o.3o.    | 6 * ♦  4  4 0  0 | 2 2  2  2  8 0 0 | 1 1  4 4 4 0 0 | 2 2 2 0
.o .o3.o3.o    | * 8 |  0  3 1  3 | 0 0  3  3  3 3 3 | 0 3  3 3 1 3 1 | 3 1 1 1
---------------+-----+------------+------------------+----------------+--------
.. .. x. ..    | 2 0 | 12  * *  * | 1 1  0  0  2 0 0 | 1 0  1 2 2 0 0 | 1 1 2 0
oo oo3oo3oo&#x | 1 1 |  * 24 *  * | 0 0  1  1  2 0 0 | 0 1  2 2 1 0 0 | 2 1 1 0
.x .. .. ..    | 0 2 |  *  * 4  * | 0 0  3  0  0 3 0 | 0 3  3 0 0 3 0 | 3 1 0 1
.. .x .. ..    | 0 2 |  *  * * 12 | 0 0  0  1  0 1 2 | 0 1  0 2 0 2 1 | 2 0 1 1
---------------+-----+------------+------------------+----------------+--------
.. o.3x. ..    | 3 0 |  3  0 0  0 | 4 *  *  *  * * * | 1 0  0 2 0 0 0 | 1 0 2 0
.. .. x.3o.    | 3 0 |  3  0 0  0 | * 4  *  *  * * * | 1 0  0 0 2 0 0 | 0 1 2 0
ox .. .. ..&#x | 1 2 |  0  2 1  0 | * * 12  *  * * * | 0 1  2 0 0 0 0 | 2 1 0 0
.. ox .. ..&#x | 1 2 |  0  2 0  1 | * *  * 12  * * * | 0 1  0 2 0 0 0 | 2 0 1 0
.. .. xo ..&#x | 2 1 |  1  2 0  0 | * *  *  * 24 * * | 0 0  1 1 1 0 0 | 1 1 1 0
.x .x .. ..    | 0 4 |  0  0 2  2 | * *  *  *  * 6 * | 0 1  0 0 0 2 0 | 2 0 0 1
.. .x3.o ..    | 0 3 |  0  0 0  3 | * *  *  *  * * 8 | 0 0  0 1 0 1 1 | 1 0 1 1
---------------+-----+------------+------------------+----------------+--------
.. o.3x.3o.    ♦ 6 0 | 12  0 0  0 | 4 4  0  0  0 0 0 | 1 *  * * * * * | 0 0 2 0
ox ox .. ..&#x ♦ 1 4 |  0  4 2  2 | 0 0  2  2  0 1 0 | * 6  * * * * * | 2 0 0 0
ox .. xo ..&#x ♦ 2 2 |  1  4 1  0 | 0 0  2  0  2 0 0 | * * 12 * * * * | 1 1 0 0
.. ox3xo ..&#x ♦ 3 3 |  3  6 0  3 | 1 0  0  3  3 0 1 | * *  * 8 * * * | 1 0 1 0
.. .. xo3oo&#x ♦ 3 1 |  3  3 0  0 | 0 1  0  0  3 0 0 | * *  * * 8 * * | 0 1 1 0
.x .x3.o ..    ♦ 0 6 |  0  0 3  6 | 0 0  0  0  0 3 2 | * *  * * * 4 * | 1 0 0 1
.. .x3.o3.o    ♦ 0 4 |  0  0 0  6 | 0 0  0  0  0 0 4 | * *  * * * * 2 | 0 0 1 1
---------------+-----+------------+------------------+----------------+--------
ox ox3xo ..&#x ♦ 3 6 |  3 12 3  6 | 1 0  6  6  6 3 2 | 0 3  3 2 0 1 0 | 4 * * *
ox .. xo3oo&#x ♦ 3 2 |  3  6 1  0 | 0 1  3  0  6 0 0 | 0 0  3 0 2 0 0 | * 4 * *
.. ox3xo3oo&#x ♦ 6 4 | 12 12 0  6 | 4 4  0  6 12 0 4 | 1 0  0 4 4 0 1 | * * 2 *
.x .x3.o3.o    ♦ 0 8 |  0  0 4 12 | 0 0  0  0  0 6 8 | 0 0  0 0 0 4 2 | * * * 1

xox3oxo3ooo&#x   → height(1,2) = height(2,3) = sqrt(5/8) = 0.790569
                   height(1,3) = 1

o..3o..3o..    | 4 * * | 3  3 1  0  0 0 | 3 3  3 3  3 0 0 0  0 0 | 1 3 1 3 3  3 0 0 0 0 | 1 1 3 1 0
.o.3.o.3.o.    | * 6 * ♦ 0  2 0  4  2 0 | 0 1  4 0  2 2 2 1  4 0 | 0 2 2 0 1  4 1 2 2 0 | 1 0 2 2 1
..o3..o3..o    | * * 4 | 0  0 1  0  3 3 | 0 0  0 3  3 0 0 3  3 3 | 0 0 0 3 3  3 0 3 1 1 | 0 1 3 1 1
---------------+-------+----------------+------------------------+----------------------+----------
x.. ... ...    | 2 0 0 | 6  * *  *  * * | 2 1  0 1  0 0 0 0  0 0 | 1 2 0 2 1  0 0 0 0 0 | 1 1 2 0 0
oo.3oo.3oo.&#x | 1 1 0 | * 12 *  *  * * | 0 1  2 0  1 0 0 0  0 0 | 0 2 1 0 1  2 0 0 0 0 | 1 0 2 1 0
o.o3o.o3o.o&#x | 1 0 1 | *  * 4  *  * * | 0 0  0 3  3 0 0 0  0 0 | 0 0 0 3 3  3 0 0 0 0 | 0 1 3 1 0
... .x. ...    | 0 2 0 | *  * * 12  * * | 0 0  1 0  0 1 1 0  1 0 | 0 1 1 0 0  1 1 1 1 0 | 1 0 1 1 1
.oo3.oo3.oo&#x | 0 1 1 | *  * *  * 12 * | 0 0  0 0  1 0 0 1  2 0 | 0 0 0 0 1  2 0 2 1 0 | 0 0 2 1 1
..x ... ...    | 0 0 2 | *  * *  *  * 6 | 0 0  0 1  0 0 0 1  0 2 | 0 0 0 2 1  0 0 2 0 1 | 0 1 2 0 1
---------------+-------+----------------+------------------------+----------------------+----------
x..3o.. ...    | 3 0 0 | 3  0 0  0  0 0 | 4 *  * *  * * * *  * * | 1 1 0 1 0  0 0 0 0 0 | 1 1 1 0 0
xo. ... ...&#x | 2 1 0 | 1  2 0  0  0 0 | * 6  * *  * * * *  * * | 0 2 0 0 1  0 0 0 0 0 | 1 0 2 0 0
... ox. ...&#x | 1 2 0 | 0  2 0  1  0 0 | * * 12 *  * * * *  * * | 0 1 1 0 0  1 0 0 0 0 | 1 0 1 1 0
x.x ... ...&#x | 2 0 2 | 1  0 2  0  0 1 | * *  * 6  * * * *  * * | 0 0 0 2 1  0 0 0 0 0 | 0 1 2 0 0
ooo3ooo3ooo&#x | 1 1 1 | 0  1 1  0  1 0 | * *  * * 12 * * *  * * | 0 0 0 0 1  2 0 0 0 0 | 0 0 2 1 0
.o.3.x. ...    | 0 3 0 | 0  0 0  3  0 0 | * *  * *  * 4 * *  * * | 0 1 0 0 0  0 1 1 0 0 | 1 0 1 0 1
... .x.3.o.    | 0 3 0 | 0  0 0  3  0 0 | * *  * *  * * 4 *  * * | 0 0 1 0 0  0 1 0 1 0 | 1 0 0 1 1
.ox ... ...&#x | 0 1 2 | 0  0 0  0  2 1 | * *  * *  * * * 6  * * | 0 0 0 0 1  0 0 2 0 0 | 0 0 2 0 1
... .xo ...&#x | 0 2 1 | 0  0 0  1  2 0 | * *  * *  * * * * 12 * | 0 0 0 0 0  1 0 1 1 0 | 0 0 1 1 1
..x3..o ...    | 0 0 3 | 0  0 0  0  0 3 | * *  * *  * * * *  * 4 | 0 0 0 1 0  0 0 1 0 1 | 0 1 1 0 1
---------------+-------+----------------+------------------------+----------------------+----------
x..3o..3o..    ♦ 4 0 0 | 6  0 0  0  0 0 | 4 0  0 0  0 0 0 0  0 0 | 1 * * * *  * * * * * | 1 1 0 0 0
xo.3ox. ...&#x ♦ 3 3 0 | 3  6 0  3  0 0 | 1 3  3 0  0 1 0 0  0 0 | * 4 * * *  * * * * * | 1 0 1 0 0
... ox.3oo.&#x ♦ 1 3 0 | 0  3 0  3  0 0 | 0 0  3 0  0 0 1 0  0 0 | * * 4 * *  * * * * * | 1 0 0 1 0
x.x3o.o ...&#x ♦ 3 0 3 | 3  0 3  0  0 3 | 1 0  0 3  0 0 0 0  0 1 | * * * 4 *  * * * * * | 0 1 1 0 0
xox ... ...&#x ♦ 2 1 2 | 1  2 2  0  2 1 | 0 1  0 1  2 0 0 1  0 0 | * * * * 6  * * * * * | 0 0 2 0 0
... oxo ...&#x ♦ 1 2 1 | 0  2 1  1  2 0 | 0 0  1 0  2 0 0 0  1 0 | * * * * * 12 * * * * | 0 0 1 1 0
.o.3.x.3.o.    ♦ 0 6 0 | 0  0 0 12  0 0 | 0 0  0 0  0 4 4 0  0 0 | * * * * *  * 1 * * * | 1 0 0 0 1
.ox3.xo ...&#x ♦ 0 3 3 | 0  0 0  3  6 3 | 0 0  0 0  0 1 0 3  3 1 | * * * * *  * * 4 * * | 0 0 1 0 1
... .xo3.oo&#x ♦ 0 3 1 | 0  0 0  3  3 0 | 0 0  0 0  0 0 1 0  3 0 | * * * * *  * * * 4 * | 0 0 0 1 1
..x3..o3..o    ♦ 0 0 4 | 0  0 0  0  0 6 | 0 0  0 0  0 0 0 0  0 4 | * * * * *  * * * * 1 | 0 1 0 0 1
---------------+-------+----------------+------------------------+----------------------+----------
xo.3ox.3oo.&#x ♦ 4 6 0 | 6 12 0 12  0 0 | 4 6 12 0  0 4 4 0  0 0 | 1 4 4 0 0  0 1 0 0 0 | 1 * * * *
x.x3o.o3o.o&#x ♦ 4 0 4 | 6  0 4  0  0 6 | 4 0  0 6  0 0 0 0  0 4 | 1 0 0 4 0  0 0 0 0 1 | * 1 * * *
xox3oxo ...&#x ♦ 3 3 3 | 3  6 3  3  6 3 | 1 3  3 3  6 1 0 3  3 1 | 0 1 0 1 3  3 0 1 0 0 | * * 4 * *
... oxo3ooo&#x ♦ 1 3 1 | 0  3 1  3  3 0 | 0 0  3 0  3 0 1 0  3 0 | 0 0 1 0 0  3 0 0 1 0 | * * * 4 *
.ox3.xo3.oo&#x ♦ 0 6 4 | 0  0 0 12 12 6 | 0 0  0 0  0 4 4 6 12 4 | 0 0 0 0 0  0 1 4 4 1 | * * * * 1

or
o..3o..3o..    & | 8 * |  3  3 1  0 | 3  3  3 3  3 0 0 | 1 3 1 3 3  3 0 | 1 1 3 1
.o.3.o.3.o.      | * 6 ♦  0  4 0  4 | 0  2  8 0  2 2 2 | 0 4 4 0 1  4 1 | 2 0 2 2
-----------------+-----+------------+------------------+----------------+--------
x.. ... ...    & | 2 0 | 12  * *  * | 2  1  0 1  0 0 0 | 1 2 0 2 1  0 0 | 1 1 2 0
oo.3oo.3oo.&#x & | 1 1 |  * 24 *  * | 0  1  2 0  1 0 0 | 0 2 1 0 1  2 0 | 1 0 2 1
o.o3o.o3o.o&#x   | 2 0 |  *  * 4  * | 0  0  0 3  3 0 0 | 0 0 0 3 3  3 0 | 0 1 3 1
... .x. ...      | 0 2 |  *  * * 12 | 0  0  2 0  0 1 1 | 0 2 2 0 0  1 1 | 2 0 1 1
-----------------+-----+------------+------------------+----------------+--------
x..3o.. ...    & | 3 0 |  3  0 0  0 | 8  *  * *  * * * | 1 1 0 1 0  0 0 | 1 1 1 0
xo. ... ...&#x & | 2 1 |  1  2 0  0 | * 12  * *  * * * | 0 2 0 0 1  0 0 | 1 0 2 0
... ox. ...&#x & | 1 2 |  0  2 0  1 | *  * 24 *  * * * | 0 1 1 0 0  1 0 | 1 0 1 1
x.x ... ...&#x   | 4 0 |  2  0 2  0 | *  *  * 6  * * * | 0 0 0 2 1  0 0 | 0 1 2 0
ooo3ooo3ooo&#x   | 2 1 |  0  2 1  0 | *  *  * * 12 * * | 0 0 0 0 1  2 0 | 0 0 2 1
.o.3.x. ...      | 0 3 |  0  0 0  3 | *  *  * *  * 4 * | 0 2 0 0 0  0 1 | 2 0 1 0
... .x.3.o.      | 0 3 |  0  0 0  3 | *  *  * *  * * 4 | 0 0 2 0 0  0 1 | 2 0 0 1
-----------------+-----+------------+------------------+----------------+--------
x..3o..3o..    & ♦ 4 0 |  6  0 0  0 | 4  0  0 0  0 0 0 | 2 * * * *  * * | 1 1 0 0
xo.3ox. ...&#x & ♦ 3 3 |  3  6 0  3 | 1  3  3 0  0 1 0 | * 8 * * *  * * | 1 0 1 0
... ox.3oo.&#x & ♦ 1 3 |  0  3 0  3 | 0  0  3 0  0 0 1 | * * 8 * *  * * | 1 0 0 1
x.x3o.o ...&#x   ♦ 6 0 |  6  0 3  0 | 2  0  0 3  0 0 0 | * * * 4 *  * * | 0 1 1 0
xox ... ...&#x   ♦ 4 1 |  2  4 2  0 | 0  2  0 1  2 0 0 | * * * * 6  * * | 0 0 2 0
... oxo ...&#x   ♦ 2 2 |  0  4 1  1 | 0  0  2 0  2 0 0 | * * * * * 12 * | 0 0 1 1
.o.3.x.3.o.      ♦ 0 6 |  0  0 0 12 | 0  0  0 0  0 4 4 | * * * * *  * 1 | 2 0 0 0
-----------------+-----+------------+------------------+----------------+--------
xo.3ox.3oo.&#x & ♦ 4 6 |  6 12 0 12 | 4  6 12 0  0 4 4 | 1 4 4 0 0  0 1 | 2 * * *
x.x3o.o3o.o&#x   ♦ 8 0 | 12  0 4  0 | 8  0  0 6  0 0 0 | 2 0 0 4 0  0 0 | * 1 * *
xox3oxo ...&#x   ♦ 6 3 |  6 12 3  3 | 2  6  6 3  6 1 0 | 0 2 0 1 3  3 0 | * * 4 *
... oxo3ooo&#x   ♦ 2 3 |  0  6 1  3 | 0  0  6 0  3 0 1 | 0 0 2 0 0  3 0 | * * * 4

top of page