Acronym	tet
TOCID symbol	T, (2)Q
Name	tetrahedron, 3D simplex (α3), pyrohedron, triangle pyramid, digonal antiprism, smaller Delone cell of face-centered cubic (fcc) lattice, regular line-scalene, regular (point-)tettene
	© ©
Circumradius	sqrt(3/8) = 0.612372
Inradius	1/sqrt(24) = 0.204124
Vertex figure	[33] = x3o
Snub derivation
Vertex layers	Layer Symmetry Subsymmetries   o3o3o o3o . o . o . o3o 1 x3o3o x3o . {3} first x . o edge first . o3o vertex first 2 o3o . opposite vertex o . x opposite edge . x3o vertex figure opposite {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 links

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