Acronym octpy, K-4.3
Name octahedral pyramid,
half of hex (its vertex-first rotunda)
Segmentochoron display
Circumradius 1/sqrt(2) = 0.707107
Inradius
wrt. tet 		1/sqrt(8) = 0.353553
Inradius
wrt. oct 		0
Lace city
in approx. ASCII-art 
    o4o    
           
o4o x4o o4o
Coordinates
    • (0, 0, 0, 1/sqrt(2))
      tip
    • (1/sqrt(2), 0, 0, 0)   & permutations and changes of sign in all but last coordinate
      octahedron base
    • (1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8))
      tip
    • (1/sqrt(8), 1/sqrt(8), -1/sqrt(8), -1/sqrt(8))   & all permutations
      octahedron base
Volume 1/12 = 0.833333
Surface sqrt(2) = 1.414214
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • at {3} between tet and tet:   120°
  • at {3} between tet and oct:   60°
Face vector 7, 18, 20, 9
Confer
more general:
n-appy  
uniform relative:
hex  
related segmentochora:
squasc  
related CRFs:
esquippidpy  
ambification:
octaco  
general polytopal classes:
Blind polytopes   segmentochora   fundamental lace prisms   lace simplices  
analogs:
rectified simplex pyramid rSn-py  
External
links 		polytopewiki  

Incidence matrix according to Dynkin symbol

ox3oo4oo&#x   → height = 1/sqrt(2) = 0.707107
(pt || oct)

o.3o.4o.    | 1 * ♦ 6  0 | 12 0 | 8 0
.o3.o4.o    | * 6 ♦ 1  4 |  4 4 | 4 1
------------+-----+------+------+----
oo3oo4oo&#x | 1 1 | 6  * |  4 0 | 4 0
.x .. ..    | 0 2 | * 12 |  1 2 | 2 1
------------+-----+------+------+----
ox .. ..&#x | 1 2 | 2  1 | 12 * | 2 0
.x3.o ..    | 0 3 | 0  3 |  * 8 | 1 1
------------+-----+------+------+----
ox3oo ..&#x ♦ 1 3 | 3  3 |  3 1 | 8 *
.x3.o4.o    ♦ 0 6 | 0 12 |  0 8 | * 1


oo3ox3oo&#x   → height = 1/sqrt(2) = 0.707107
(pt || oct)

o.3o.3o.    | 1 * ♦ 6  0 | 12 0 0 | 4 4 0
.o3.o3.o    | * 6 ♦ 1  4 |  4 2 2 | 2 2 1
------------+-----+------+--------+------
oo3oo3oo&#x | 1 1 | 6  * |  4 0 0 | 2 2 0
.. .x ..    | 0 2 | * 12 |  1 1 1 | 1 1 1
------------+-----+------+--------+------
.. ox ..&#x | 1 2 | 2  1 | 12 * * | 1 1 0
.o3.x ..    | 0 3 | 0  3 |  * 4 * | 1 0 1
.. .x3.o    | 0 3 | 0  3 |  * * 4 | 0 1 1
------------+-----+------+--------+------
oo3ox ..&#x ♦ 1 3 | 3  3 |  3 1 0 | 4 * *
.. ox3oo&#x ♦ 1 3 | 3  3 |  3 0 1 | * 4 *
.o3.x3.o    ♦ 0 6 | 0 12 |  0 4 4 | * * 1


xoo3oxo&#x   → height(1,2) = sqrt(2/3) = 0.816497
               height(1,3) = height(2,3) = 1/sqrt(2) = 0.707107
(({3} || dual {3}) || pt)

o..3o..    | 3 * * ♦ 2 2 1 0 0 | 1 2 1 2 2 0 0 | 1 1 2 1 0
.o.3.o.    | * 3 * ♦ 0 2 0 2 1 | 0 1 2 0 2 1 2 | 1 0 1 2 1
..o3..o    | * * 1 ♦ 0 0 3 0 3 | 0 0 0 3 6 0 3 | 0 1 3 3 1
-----------+-------+-----------+---------------+----------
x.. ...    | 2 0 0 | 3 * * * * | 1 1 0 1 0 0 0 | 1 1 1 0 0
oo.3oo.&#x | 1 1 0 | * 6 * * * | 0 1 1 0 1 0 0 | 1 0 1 1 0
o.o3o.o&#x | 1 0 1 | * * 3 * * | 0 0 0 2 2 0 0 | 0 1 2 1 0
... .x.    | 0 2 0 | * * * 3 * | 0 0 1 0 0 1 1 | 1 0 0 1 1
.oo3.oo&#x | 0 1 1 | * * * * 3 | 0 0 0 0 2 0 2 | 0 0 1 2 1
-----------+-------+-----------+---------------+----------
x..3o..    | 3 0 0 | 3 0 0 0 0 | 1 * * * * * * | 1 1 0 0 0
xo. ...&#x | 2 1 0 | 1 2 0 0 0 | * 3 * * * * * | 1 0 1 0 0
... ox.&#x | 1 2 0 | 0 2 0 1 0 | * * 3 * * * * | 1 0 0 1 0
x.o ...&#x | 2 0 1 | 1 0 2 0 0 | * * * 3 * * * | 0 1 1 0 0
ooo3ooo&#x | 1 1 1 | 0 1 1 0 1 | * * * * 6 * * | 0 0 1 1 0
.o.3.x.    | 0 3 0 | 0 0 0 3 0 | * * * * * 1 * | 1 0 0 0 1
... .xo&#x | 0 2 1 | 0 0 0 1 2 | * * * * * * 3 | 0 0 0 1 1
-----------+-------+-----------+---------------+----------
xo.3ox.&#x ♦ 3 3 0 | 3 6 0 3 0 | 1 3 3 0 0 1 0 | 1 * * * *
x.o3o.o&#x ♦ 3 0 1 | 3 0 3 0 0 | 1 0 0 3 0 0 0 | * 1 * * *
xoo ...&#x ♦ 2 1 1 | 1 2 2 0 1 | 0 1 0 1 2 0 0 | * * 3 * *
... oxo&#x ♦ 1 2 1 | 0 2 1 1 2 | 0 0 1 0 2 0 1 | * * * 3 *
.oo3.xo&#x ♦ 0 3 1 | 0 0 0 3 3 | 0 0 0 0 0 1 3 | * * * * 1

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