How to see ISEA with QGIS?

Question

Using the spatial reference +proj=isea and comparing with others, in separate tables to avoid confusion in the QGIS renderization. But no visualization... is a QGIS bug? For example:

CREATE TABLE test1_b AS    -- Pure WGS84
  SELECT 1 AS gid,
         ST_SetSRID(ST_GeomFromGeoHash('d2g6b'), 4326) AS geom
;
CREATE TABLE test1_c AS    -- Same but Shere instead ellipsoid
  SELECT 1 AS gid,
       ST_Transform(
          ST_SetSRID(ST_GeomFromGeoHash('d2g6c'),4326),
          '+proj=lonlat +ellps=sphere'
       ) AS geom
;
CREATE TABLE test1_f AS   -- ISEA, that is also Shere
  SELECT 1 AS gid, 
        ST_Transform(
           ST_SetSRID(ST_GeomFromGeoHash('d2g6f'),4326),
           '+proj=isea'
        ) AS geom
;

QGIS v3 only shows test1_b and test1_c:

---

Notes

• Geohashes d2g6b, d2g6c and d2g6f are horizontal neighbors. As showed before, the ISEA projection use ellps=sphere, and as showed by illustration (d2g6c box), QGIS can plot ellps=sphere... I supposed that QGIS can plot d2g6c also, using similar infrastructure.

• Supposing that d2g6f is a small box contained into an ISEA's icosahedron face... So, no risc of "coordinate jump".

• In the related questions, "How to use ISEA projection?" and "DGGS projections with PostGIS or pgLatLon", no clues about visualization.

• Double transform also not works, is not valid to transform ISEA back to any simple SRID.

• Dump to text seems good: select st_astext(geom) from test1_f results the WKT below

 POLYGON((
  -9457665.085273389 722136.153457215,
  -9460296.69550779  726590.233366592,
  -9456290.810885958 728872.6605645764,
  -9453658.792895738 724419.0107246666,
  -9457665.085273389 722136.153457215
))

---

(edit)

Seems that "no inverse → no visualization"

As Even Rouault commented here,

the reason is much likely that only the forward method
(geographic coordinates → projected coordinates) is implemented,
whereas QGIS also requires the inverse method to be implemented.

Answer 1

Maybe it is only a missing parameter, needed to tell PostGIS that you want it to use use a sphererical projection.

In your SQL, please try using:

'+proj=isea +ellps=sphere'

instead of the mere

'+proj=isea'

that is:

CREATE TABLE test1_f AS   -- ISEA, that is also Shere
  SELECT 1 AS gid, 
        ST_Transform(
           ST_SetSRID(ST_GeomFromGeoHash('d2g6f'),4326),
           '+proj=isea +ellps=sphere'
        ) AS geom
;

Answer 2

We can try again using fresh QGIS, with the new implementation of PROJ, version 9.5 or later. It say "Available forms: Forward and inverse, spherical".

The inverse was a years-old issue, finally implemented by Jerome St-Louis in this pull request of Aug 2024.