Acronym	snit
Name	pyritohedron, pyritosnub tetrahedron, vertex alternated toe
Circumradius	sqrt(5/2) = 1.581139
Snub derivation
Face vector	12, 30, 20
Confer	more general: general pyritohedral ike   uniform variant: ike   general polytopal classes: isogonal
External links

This polyhedron is isogonal only. It reflects the mere alternated faceting of the above depicted snub derivation wrt. a vertex alternation with starting figure toe. However, it could be resized to all unit-sized edges, then resulting in the regular ike.

It also can be considered to be the special case Qqo oQq qoQ&#zh (where Q = 2q) of the general pyritohedral ike.

Incidence matrix according to Dynkin symbol

s3s3s

demi( . . . ) | 12 | 1  2  2 | 1 1  3
--------------+----+---------+-------
      s 2 s   |  2 | 6  *  * | 0 0  2  q
sefa( s3s . ) |  2 | * 12  * | 1 0  1  h
sefa( . s3s ) |  2 | *  * 12 | 0 1  1  h
--------------+----+---------+-------
      s3s .   ♦  3 | 0  3  0 | 4 *  *  h3o
      . s3s   ♦  3 | 0  0  3 | * 4  *  h3o
sefa( s3s3s ) |  3 | 1  1  1 | * * 12  oq&#h

starting figure: x3x3x

s3s4o

demi( . . . ) | 12 | 1  4 | 2  3
--------------+----+------+-----
      . s4o   |  2 | 6  * | 0  2  q
sefa( s3s . ) |  2 | * 24 | 1  1  h
--------------+----+------+-----
      s3s .   ♦  3 | 0  3 | 8  *  h3o
sefa( s3s4o ) |  3 | 1  2 | * 12  oq&#h

starting figure: x3x4o

s3s4/3o

demi( . .   . ) | 12 | 1  4 | 2  3
----------------+----+------+-----
      . s4/3o   |  2 | 6  * | 0  2  q
sefa( s3s   . ) |  2 | * 24 | 1  1  h
----------------+----+------+-----
      s3s   .   ♦  3 | 0  3 | 8  *  h3o
sefa( s3s4/3o ) |  3 | 1  2 | * 12  oq&#h

starting figure: x3x4/3o

qQo oqQ Qoq&#zh   → height = 0
                    where Q = 2q = sqrt(8) = 2.828427 (pseudo)
(tegum sum 3 mutually perp. (q,Q)-rectangles)

o.. o.. o..    | 4 * * | 1 2 2 0 0 0 | 1 2 2 0
.o. .o. .o.    | * 4 * | 0 2 0 1 2 0 | 2 2 0 1
..o ..o ..o    | * * 4 | 0 0 2 0 2 1 | 0 2 1 2
---------------+-------+-------------+--------
q.. ... ...    | 2 0 0 | 2 * * * * * | 0 0 2 0
oo. oo. oo.&#h | 1 1 0 | * 8 * * * * | 1 1 0 0
o.o o.o o.o&#h | 1 0 1 | * * 8 * * * | 0 1 1 0
... .q. ...    | 0 2 0 | * * * 2 * * | 2 0 0 0
.oo .oo .oo&#h | 0 1 1 | * * * * 8 * | 0 1 0 1
... ... ..q    | 0 0 2 | * * * * * 2 | 0 0 0 2
---------------+-------+-------------+--------
... oq. ...&#h | 1 2 0 | 0 2 0 1 0 0 | 4 * * *  oq&#h
ooo ooo ooo&#h | 1 1 1 | 0 1 1 0 1 0 | * 8 * *  h3o
q.o ... ...&#h | 2 0 1 | 1 0 2 0 0 0 | * * 4 *  oq&#h
... ... .oq&#h | 0 1 2 | 0 0 0 0 2 1 | * * * 4  oq&#h