Acronym tet
TOCID symbol T, (2)Q
Name tetrahedron,
3D simplex3),
pyrohedron,
triangle pyramid,
digonal antiprism,
smaller Delone cell of face-centered cubic (fcc) lattice,
regular line-scalene,
regular (point-)tettene

` © ©`
Vertex figure [33] = x3o
Snub derivation
Vertex layers
 Layer Symmetry Subsymmetries o3o3o o3o . o . o . o3o 1 x3o3o x3o .{3} first x . oedge first . o3overtex first 2 o3o .opposite vertex o . xopposite edge . x3overtex figureopposite {3}
Lace city
in approx. ASCII-art
``` o
x o
```
Coordinates (1/sqrt(8), 1/sqrt(8), 1/sqrt(8))   & all even permutations, all even changes of sign
General of army (is itself convex)
Colonel of regiment (is itself locally convex – no other uniform polyhedral members)
Dual (selfdual, in different orientation)
Confer
general pyramids:
n/d-py
general antiprisms:
n/d-ap
Grünbaumian relatives:
2tet   3tet   4tet   6tet
blends:
tridpy
compounds:
so   ki   e   sis   snu   dis
general polytopal classes:
deltahedra   regular   simplex
External

Incidence matrix according to Dynkin symbol

```x3o3o

. . . | 4 | 3 | 3
------+---+---+--
x . . | 2 | 6 | 2
------+---+---+--
x3o . | 3 | 3 | 4
```

```x3o3/2o

. .   . | 4 | 3 | 3
--------+---+---+--
x .   . | 2 | 6 | 2
--------+---+---+--
x3o   . | 3 | 3 | 4
```

```x3/2o3o

.   . . | 4 | 3 | 3
--------+---+---+--
x   . . | 2 | 6 | 2
--------+---+---+--
x3/2o . | 3 | 3 | 4
```

```x3/2o3/2o

.   .   . | 4 | 3 | 3
----------+---+---+--
x   .   . | 2 | 6 | 2
----------+---+---+--
x3/2o   . | 3 | 3 | 4
```

```s4o3o

demi( . . . ) | 4 | 3 | 3
--------------+---+---+--
s4o .   ♦ 2 | 6 | 2
--------------+---+---+--
sefa( s4o3o ) | 3 | 3 | 4
```

```s2s4o

demi( . . . ) | 4 | 2 1 | 3
--------------+---+-----+--
s2s .   ♦ 2 | 4 * | 2
. s4o   ♦ 2 | * 2 | 2
--------------+---+-----+--
sefa( s2s4o ) | 3 | 2 1 | 4
```

```s2s2s

demi( . . . ) | 4 | 1 1 1 | 3
--------------+---+-------+--
s2s .   ♦ 2 | 2 * * | 2
s 2 s   ♦ 2 | * 2 * | 2
. s2s   ♦ 2 | * * 2 | 2
--------------+---+-------+--
sefa( s2s2s ) | 3 | 1 1 1 | 4
```

```xo3oo&#x   → height = sqrt(2/3) = 0.816497
({3} || pt)

o.3o.    | 3 * | 2 1 | 1 2
.o3.o    | * 1 | 0 3 | 0 3
---------+-----+-----+----
x. ..    | 2 0 | 3 * | 1 1
oo3oo&#x | 1 1 | * 3 | 0 2
---------+-----+-----+----
x.3o.    | 3 0 | 3 0 | 1 *
xo ..&#x | 2 1 | 1 2 | * 3
```

```xo ox&#x   → height = 1/sqrt(2) = 0.707107
(line || perp line)

o. o.    | 2 * | 1 2 0 | 2 1
.o .o    | * 2 | 0 2 1 | 1 2
---------+-----+-------+----
x. ..    | 2 0 | 1 * * | 2 0
oo oo&#x | 1 1 | * 4 * | 1 1
.. .x    | 0 2 | * * 1 | 0 2
---------+-----+-------+----
xo ..&#x | 2 1 | 1 2 0 | 2 *
.. ox&#x | 1 2 | 0 2 1 | * 2
```

```oxo&#x   → height(1,2) = height(2,3) = sqrt(3)/2 = 0.866025
height(1,3) = 1
( (pt || line) || pt)

o..    | 1 * * | 2 1 0 0 | 1 2 0
.o.    | * 2 * | 1 0 1 1 | 1 1 1
..o    | * * 1 | 0 1 0 2 | 0 2 1
-------+-------+---------+------
oo.&#x | 1 1 0 | 2 * * * | 1 1 0
o.o&#x | 1 0 1 | * 1 * * | 0 2 0
.x.    | 0 2 0 | * * 1 * | 1 0 1
.oo&#x | 0 1 1 | * * * 2 | 0 1 1
-------+-------+---------+------
ox.&#x | 1 2 0 | 2 0 1 0 | 1 * *
ooo&#x | 1 1 1 | 1 1 0 1 | * 2 *
.xo&#x | 0 2 1 | 0 0 1 2 | * * 1
```