Acronym recta
Name rectangular alterprism,
rectangular trapezoprism
Circumradius sqrt[c2+(a+b)2/2]/2
Snub derivation

case: (a,b,c) = (x,w,q)
Lace city
in approx. ASCII-art
a     a
  b b
Coordinates
  • (a/2, b/2; sqrt[c2-(b-a)2/2]/2)    & all changes of sign in first 2 coords
  • (b/2, a/2; -sqrt[c2-(b-a)2/2]/2)   & all changes of sign in first 2 coords
Dihedral angles
(at margins)
  • at a-edge (short side of rectangle):   arccos(1/sqrt[4c2/(b-a)2-1])
  • at b-edge (long side of rectangle):   arccos(-1/sqrt[4c2/(b-a)2-1])
  • at c-edge (lacings):   arccos(1/[4c2/(b-a)2-1])
Confer
regular variant:
cube  

The variant with (a,b,c) = (x,w,q) occurs as the mere base-edge alternated faceting s2s4x obtained from the op.


Incidence matrix according to Dynkin symbol

ab ba&#c   → height = sqrt[c2-(b-a)2/2]
             a < b
             c > (b-a)/sqrt(2)

o. o.    | 4 * | 1 1 1 0 0 | 1 1 1 0
.o .o    | * 4 | 0 0 1 1 1 | 0 1 1 1
---------+-----+-----------+--------
a. ..    | 2 0 | 2 * * * * | 1 1 0 0
.. b.    | 2 0 | * 2 * * * | 1 0 1 0
oo oo&#c | 1 1 | * * 4 * * | 0 1 1 0
.b ..    | 0 2 | * * * 2 * | 0 1 0 1
.. .a    | 0 2 | * * * * 2 | 0 0 1 1
---------+-----+-----------+--------
a. b.    | 4 0 | 2 2 0 0 0 | 1 * * *  rectangle
ab ..&#c | 2 2 | 1 0 2 1 0 | * 2 * *  trapezium
.. ba&#c | 2 2 | 0 1 2 0 1 | * * 2 *  trapezium
.b .a    | 0 4 | 0 0 0 2 2 | * * * 1  rectangle
or
o. o.    & | 8 | 1 1 1 | 1 2
-----------+---+-------+----
a. ..    & | 2 | 4 * * | 1 1
.. b.    & | 2 | * 4 * | 1 1
oo oo&#c   | 2 | * * 4 | 0 2
-----------+---+-------+----
a. b.    & | 4 | 2 2 0 | 2 *  rectangle
ab ..&#c   | 4 | 1 1 2 | * 4  trapezium

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