diff --git a/src/h5core/h5t_adjacencies_tetm.c b/src/h5core/h5t_adjacencies_tetm.c
index 839c7de..1bdcc98 100644
--- a/src/h5core/h5t_adjacencies_tetm.c
+++ b/src/h5core/h5t_adjacencies_tetm.c
@@ -32,7 +32,7 @@ compute_elems_of_vertices (
 		int face_idx;
 		int num_faces = t->ref_element->num_faces[0];
 		for (face_idx = 0; face_idx < num_faces; face_idx++) {
-			h5_id_t vidx = el->local_vids[face_idx];
+			h5_id_t vidx = el->local_vertex_indices[face_idx];
 			TRY( h5priv_append_to_idlist (
 				     f,
 				     &t->vertices_data[vidx].tv,
@@ -118,7 +118,7 @@ compute_children_of_edge (
 			TRY( t->methods.store->get_direct_children_of_edge (
 				      f,
 				      face_idx,
-				      tet->local_child_eid,
+				      tet->local_child_idx,
 				      kids) );
 			TRY( compute_children_of_edge (f, kids[0], children) );
 			TRY( compute_children_of_edge (f, kids[1], children) );
@@ -157,7 +157,7 @@ compute_sections_of_edge (
 			TRY( t->methods.store->get_direct_children_of_edge (
 				     f,
 				     face_id,
-				     tet->local_child_eid,
+				     tet->local_child_idx,
 				     kids) );
 			TRY( compute_sections_of_edge (f, kids[0], children) );
 			TRY( compute_sections_of_edge (f, kids[1], children) );
@@ -256,7 +256,7 @@ compute_children_of_triangle (
 			TRY( compute_direct_children_of_triangle (
 				      f,
 				      face_idx,
-				      tet->local_child_eid,
+				      tet->local_child_idx,
 				      dids) );
 			TRY( compute_children_of_triangle (f, dids[0], children) );
 			TRY( compute_children_of_triangle (f, dids[1], children) );
@@ -293,7 +293,7 @@ compute_sections_of_triangle (
 			TRY( compute_direct_children_of_triangle (
 				     f,
 				     face_idx,
-				     tet->local_child_eid,
+				     tet->local_child_idx,
 				     dids) );
 			TRY( compute_sections_of_triangle (f, dids[0], children) );
 			TRY( compute_sections_of_triangle (f, dids[1], children) );
diff --git a/src/h5core/h5t_adjacencies_trim.c b/src/h5core/h5t_adjacencies_trim.c
index 17598d7..0e9d11f 100644
--- a/src/h5core/h5t_adjacencies_trim.c
+++ b/src/h5core/h5t_adjacencies_trim.c
@@ -32,7 +32,7 @@ compute_elems_of_vertices (
 		int face_idx;
 		int num_faces = t->ref_element->num_faces[0];
 		for (face_idx = 0; face_idx < num_faces; face_idx++) {
-			h5_id_t vidx = el->local_vids[face_idx];
+			h5_id_t vidx = el->local_vertex_indices[face_idx];
 			TRY( h5priv_append_to_idlist (
 				     f,
 				     &t->vertices_data[vidx].tv,
@@ -98,7 +98,7 @@ compute_children_of_edge (
 			TRY ( t->methods.store->get_direct_children_of_edge (
 				      f,
 				      face_idx,
-				      el->local_child_eid,
+				      el->local_child_idx,
 				      kids ) );
 			TRY ( compute_children_of_edge (
 				      f, kids[0], children ) );
@@ -140,7 +140,7 @@ compute_sections_of_edge (
 			TRY ( t->methods.store->get_direct_children_of_edge (
 				      f,
 				      face_id,
-				      el->local_child_eid,
+				      el->local_child_idx,
 				      kids ) );
 			TRY ( compute_sections_of_edge (
 				      f, kids[0], children ) );
diff --git a/src/h5core/h5t_core_private.h b/src/h5core/h5t_core_private.h
index 9ed749e..e013063 100644
--- a/src/h5core/h5t_core_private.h
+++ b/src/h5core/h5t_core_private.h
@@ -4,18 +4,19 @@
 #define H5T_CONTAINER_GRPNAME	"Topo"
 
 #include "h5t_openclose_private.h"
-#include "h5t_tetm_adjacencies_private.h"
-#include "h5t_tetm_retrieve_private.h"
-#include "h5t_tetm_store_private.h"
-#include "h5t_trim_adjacencies_private.h"
-#include "h5t_trim_retrieve_private.h"
-#include "h5t_trim_store_private.h"
+#include "h5t_adjacencies_tetm_private.h"
+#include "h5t_adjacencies_trim_private.h"
+
 #include "h5t_consts_private.h"
 #include "h5t_errorhandling_private.h"
 #include "h5t_hsearch_private.h"
 #include "h5t_map_private.h"
 #include "h5t_readwrite_private.h"
-#include "h5t_storemesh_private.h"
+#include "h5t_retrieve_tetm_private.h"
+#include "h5t_retrieve_trim_private.h"
+#include "h5t_store_private.h"
+#include "h5t_store_tetm_private.h"
+#include "h5t_store_trim_private.h"
 #include "h5t_tags_private.h"
 
 #include "h5t_types_private.h"
diff --git a/src/h5core/h5t_errorhandling.c b/src/h5core/h5t_errorhandling.c
index 0da313a..f2a6c35 100644
--- a/src/h5core/h5t_errorhandling.c
+++ b/src/h5core/h5t_errorhandling.c
@@ -10,18 +10,19 @@ const char* ERR_ELEM_NEXIST = "Element with local vertex IDs (%s) doesn't exist!
 h5_err_t
 h5tpriv_error_local_elem_nexist (
 	h5_file_t* const f,
-	h5_id_t local_vids[]
+	h5_id_t local_vertex_indices[]
 	) {
 	h5t_fdata_t* t = f->t;
 	char s[1024];
 
-	int num_chars_printed = snprintf (s, sizeof(s), "%lld,", local_vids[0]);
+	int num_chars_printed = snprintf (s, sizeof(s), "%lld,",
+					  local_vertex_indices[0]);
 	int i;
 	int num_vertices = t->ref_element->num_faces[0];
 	for (i = 1; i < num_vertices; i++) {
 		num_chars_printed += snprintf (
 			s + num_chars_printed, sizeof (s) - num_chars_printed,
-			"%lld,", local_vids[i]);
+			"%lld,", local_vertex_indices[i]);
 		if ((sizeof (s) - num_chars_printed) < 32) {
 			// buffer to small
 			return h5_error_internal (f, __FILE__, __func__, __LINE__);
diff --git a/src/h5core/h5t_errorhandling_private.h b/src/h5core/h5t_errorhandling_private.h
index 830a318..d18eb7c 100644
--- a/src/h5core/h5t_errorhandling_private.h
+++ b/src/h5core/h5t_errorhandling_private.h
@@ -4,7 +4,7 @@
 h5_err_t
 h5tpriv_error_local_elem_nexist (
 	h5_file_t * const f,
-	h5_id_t local_vids[]
+	h5_id_t local_vertex_indices[]
 	);
 
 #define h5tpriv_error_undef_mesh( f )		\
@@ -41,12 +41,12 @@ h5tpriv_error_local_elem_nexist (
 		"Triangle with global vertex ids (%lld,%lld,%lld) doesn't exist!", \
 		vids[0], vids[1], vids[2] );
 
-#define h5tpriv_error_local_triangle_nexist( f, local_vids )			\
+#define h5tpriv_error_local_triangle_nexist( f, indices )	\
 	h5_error(							\
 		f,							\
 		H5_ERR_NOENTRY,						\
 		"Triangle with global vertex ids (%lld,%lld,%lld) doesn't exist!", \
-		local_vids[0], local_vids[1], local_vids[2] );
+		indices[0], indices[1], indices[2] );
 
 
 #define h5tpriv_error_store_boundaryface_local_id( f, local_fid )	     \
diff --git a/src/h5core/h5t_hsearch.c b/src/h5core/h5t_hsearch.c
index e6c773a..cd0858c 100644
--- a/src/h5core/h5t_hsearch.c
+++ b/src/h5core/h5t_hsearch.c
@@ -305,7 +305,7 @@ h5tpriv_find_tv2 (
 	/*
 	  map (cid,el_idx) to local index of vertex
 	*/
-	h5_id_t vertex_idx = f->t->elems_ldta[elem_idx].local_vids[face_idx];
+	h5_id_t vertex_idx = f->t->elems_ldta[elem_idx].local_vertex_indices[face_idx];
 	*retval = &f->t->vertices_data[vertex_idx].tv;
 
 	return H5_SUCCESS;
diff --git a/src/h5core/h5t_map.c b/src/h5core/h5t_map.c
index b6109e3..6dcb3b6 100644
--- a/src/h5core/h5t_map.c
+++ b/src/h5core/h5t_map.c
@@ -107,10 +107,10 @@ h5tpriv_get_local_vid (
   element id. For triangles \c i is in \c [0,1,2], for tetraheda \c i is in
   \c [0,1,2,3].
 
-  t->elems_ldta[local_eid].local_vids[i]
+
 */
 #define get_vertex_of_elem( f, i, eid ) \
-	(f->t->vertices[ f->t->elems_ldta[eid].local_vids[i] ].P)
+	(f->t->vertices[ f->t->elems_ldta[eid].local_vertex_indices[i] ].P)
 
 
 
@@ -245,29 +245,29 @@ h5tpriv_sort_elems (
 }
 
 /*!
-  Sort (small) array of local vertex ids geometrically. 
+  Sort (small) array of local vertex indices geometrically. 
  */
 h5_err_t
-h5tpriv_sort_local_vids (
+h5tpriv_sort_local_vertex_indices (
 	h5_file_t* const f,
-	h5_id_t* const local_vids,		/* IN/OUT: local vertex ids */	
-	const h5_size_t size			/* size of array */
+	h5_id_t* const indices,		/* IN/OUT: local vertex indices */	
+	const h5_size_t size		/* size of array */
 	) {
 	h5t_fdata_t* t = f->t;
 
 	h5_size_t i;
 	for (i = 1; i < size; ++i) {
-		h5_id_t local_vid = local_vids[i];
+		h5_id_t idx = indices[i];
 
 		h5_id_t j = i;
 		while ((j >= 1 ) && cmp_vertices (
-			       t->vertices[local_vid].P,
-			       t->vertices[local_vids[j-1]].P 
+			       t->vertices[idx].P,
+			       t->vertices[indices[j-1]].P 
 			       ) < 0 ) {
-			local_vids[j] = local_vids[j-1];
+			indices[j] = indices[j-1];
 			--j;
 		}
-		local_vids[j] = local_vid;
+		indices[j] = idx;
 	}
 	return H5_SUCCESS;
 }
@@ -280,20 +280,20 @@ h5tpriv_sort_local_vids (
 static h5_id_t
 search_elem (
 	h5_file_t* const f,
-	h5_id_t* const local_vids	/* local vertex ids */
+	h5_id_t* const vertex_indices	/* local vertex ids */
 	) {
 	h5t_fdata_t* t = f->t;
 	int num_vertices = t->ref_element->num_faces[0];
-	h5tpriv_sort_local_vids ( f, local_vids, num_vertices );
+	h5tpriv_sort_local_vertex_indices ( f, vertex_indices, num_vertices );
 
 	register h5_id_t low = 0;
 	register h5_id_t high = t->sorted_elems[0].num_items - 1;
-	register h5_id_t *elem1 = local_vids;
+	register h5_id_t *elem1 = vertex_indices;
 	while (low <= high) {
 		register int mid = (low + high) / 2;
 
 		h5_id_t local_eid = t->sorted_elems[0].items[mid];
-		h5_id_t *elem2 = t->elems_ldta[local_eid].local_vids;
+		h5_id_t *elem2 = t->elems_ldta[local_eid].local_vertex_indices;
 		int diff = vcmp_elems ( f, elem1, elem2 );
            	if (diff < 0)
                		high = mid - 1;
@@ -302,58 +302,58 @@ search_elem (
            	else
                		return mid; // found
        	}
-	return h5tpriv_error_local_elem_nexist (f, local_vids);
+	return h5tpriv_error_local_elem_nexist (f, vertex_indices);
 }
 
 /*!
-  Map a global vertex id to corresponding local vertex id.
+  Map a global vertex index to corresponding local index.
 */
 h5_id_t
-h5t_map_global_vid2local (
+h5t_map_global_vertex_idx2local (
 	h5_file_t* const f,
-	const h5_id_t global_id
+	const h5_id_t global_idx
 	) {
 	h5t_fdata_t* t = f->t;
 
-	h5_id_t local_id = h5priv_search_idmap (&t->map_vertex_g2l, global_id);
-	if (local_id < 0) 
-		return h5tpriv_error_global_id_nexist (f, "vertex", global_id);
-	return local_id;
+	h5_id_t local_idx = h5priv_search_idmap (&t->map_vertex_g2l, global_idx);
+	if (local_idx < 0) 
+		return h5tpriv_error_global_id_nexist (f, "vertex", global_idx);
+	return local_idx;
 }
 
 h5_err_t
-h5t_map_global_vids2local (
+h5t_map_global_vertex_indices2local (
 	h5_file_t* const f,
-	const h5_id_t* const global_vids,
+	const h5_id_t* const global_indices,
 	const h5_id_t size,
-	h5_id_t* const local_vids
+	h5_id_t* const local_indices
 	) {
 	h5_id_t i;
 	for (i = 0; i < size; i++) {
-		TRY( (local_vids[i] = h5t_map_global_vid2local (
-				f, global_vids[i])) );
+		TRY( (local_indices[i] = h5t_map_global_vertex_idx2local (
+				f, global_indices[i])) );
 	}
 	return H5_SUCCESS;
 }
 
 /*!
-  Get local element id for an element given by its global id.
+  Get local element idx of element given by its global idx.
 
   \param[in]	f		File handle
-  \param[in]	global_eid	Global element id
+  \param[in]	global_idx	Global element id
 
   \return	Local element id or error code.
 */
 h5_id_t
-h5t_map_global_eid2local (
+h5t_map_global_elem_idx2local (
 	h5_file_t* const f,
-	const h5_id_t global_eid
+	const h5_id_t global_idx
 	) {
 	h5t_fdata_t* t = f->t;
-	h5_id_t local_eid = h5priv_search_idmap (&t->map_elem_g2l, global_eid);
-	if (local_eid < 0) 
-		return h5tpriv_error_global_id_nexist (f, "elem", global_eid);
-	return local_eid;
+	h5_id_t local_idx = h5priv_search_idmap (&t->map_elem_g2l, global_idx);
+	if (local_idx < 0) 
+		return h5tpriv_error_global_id_nexist (f, "elem", global_idx);
+	return local_idx;
 }
 
 h5_err_t
@@ -366,7 +366,7 @@ h5tpriv_rebuild_global_2_local_map_of_vertices (
 		t->num_vertices[t->cur_level-1] : 0;
 	for (; local_vid < t->num_vertices[t->num_levels-1]; local_vid++) {
 		t->map_vertex_g2l.items[local_vid].global_id =
-			t->vertices[local_vid].global_vid; 
+			t->vertices[local_vid].global_idx; 
 		t->map_vertex_g2l.items[local_vid].local_id = local_vid;
 		t->map_vertex_g2l.num_items++;
 	}
@@ -393,7 +393,7 @@ h5tpriv_rebuild_global_2_local_map_of_elems (
 		     elemp+=offset) {
 		h5_elem_t* elem = (h5_elem_t*)elemp;
 		
-		item->global_id = elem->global_eid; 
+		item->global_id = elem->global_idx; 
 		item->local_id = local_eid;
 		t->map_elem_g2l.num_items++;
 	}
@@ -426,7 +426,7 @@ h5t_get_vertex_indices_of_entity (
 	int i;
 	for (i = 0; i < num_vertices; i++) {
 		int idx = ref_element->map[dim][face_idx][i];
-		vertex_indices[i] = el->local_vids[idx];
+		vertex_indices[i] = el->local_vertex_indices[idx];
 	}
 	return H5_SUCCESS;
 }
@@ -453,7 +453,7 @@ h5t_get_vertex_index_of_vertex2 (
 	const h5t_ref_element_t* ref_element = f->t->ref_element;
 	h5_elem_ldta_t *el = &f->t->elems_ldta[elem_idx];
 
- 	vertex_indices[0] = el->local_vids[ref_element->map[0][face_idx][0]];
+ 	vertex_indices[0] = el->local_vertex_indices[ref_element->map[0][face_idx][0]];
 	return H5_SUCCESS;
 }
 
@@ -489,8 +489,8 @@ h5t_get_vertex_indices_of_edge2 (
 	const h5t_ref_element_t* ref_element = f->t->ref_element;
 	h5_elem_ldta_t* el = &f->t->elems_ldta[elem_idx];
 
- 	vertex_indices[0] = el->local_vids[ref_element->map[1][face_idx][0]];
-	vertex_indices[1] = el->local_vids[ref_element->map[1][face_idx][1]];
+ 	vertex_indices[0] = el->local_vertex_indices[ref_element->map[1][face_idx][0]];
+	vertex_indices[1] = el->local_vertex_indices[ref_element->map[1][face_idx][1]];
 	return H5_SUCCESS;
 }
 
@@ -516,9 +516,9 @@ h5t_get_vertex_indices_of_triangle2 (
 	const h5t_ref_element_t* ref_element = f->t->ref_element;
 	h5_elem_ldta_t* el = &f->t->elems_ldta[elem_idx];
 
- 	vertex_indices[0] = el->local_vids[ref_element->map[2][face_idx][0]];
-	vertex_indices[1] = el->local_vids[ref_element->map[2][face_idx][1]];
-	vertex_indices[2] = el->local_vids[ref_element->map[2][face_idx][2]];
+ 	vertex_indices[0] = el->local_vertex_indices[ref_element->map[2][face_idx][0]];
+	vertex_indices[1] = el->local_vertex_indices[ref_element->map[2][face_idx][1]];
+	vertex_indices[2] = el->local_vertex_indices[ref_element->map[2][face_idx][2]];
 
 	return H5_SUCCESS;
 }
@@ -533,10 +533,10 @@ h5t_get_vertex_indices_of_tet (
 	const h5t_ref_element_t* ref_element = f->t->ref_element;
 	h5_elem_ldta_t* el = &f->t->elems_ldta[elem_idx];
 
- 	vertex_indices[0] = el->local_vids[ref_element->map[3][0][0]];
-	vertex_indices[1] = el->local_vids[ref_element->map[3][0][1]];
-	vertex_indices[2] = el->local_vids[ref_element->map[3][0][2]];
-	vertex_indices[3] = el->local_vids[ref_element->map[3][0][3]];
+ 	vertex_indices[0] = el->local_vertex_indices[ref_element->map[3][0][0]];
+	vertex_indices[1] = el->local_vertex_indices[ref_element->map[3][0][1]];
+	vertex_indices[2] = el->local_vertex_indices[ref_element->map[3][0][2]];
+	vertex_indices[3] = el->local_vertex_indices[ref_element->map[3][0][3]];
 
 	return H5_SUCCESS;
 }
diff --git a/src/h5core/h5t_map_private.h b/src/h5core/h5t_map_private.h
index 31259dd..589c179 100644
--- a/src/h5core/h5t_map_private.h
+++ b/src/h5core/h5t_map_private.h
@@ -2,9 +2,9 @@
 #define __H5T_MAP_PRIVATE_H
 
 h5_err_t
-h5tpriv_sort_local_vids (
+h5tpriv_sort_local_vertex_indices (
 	h5_file_t * const f,
-	h5_id_t * const local_vids,
+	h5_id_t * const indices,
 	const h5_size_t size
 	);
 
diff --git a/src/h5core/h5t_openclose.c b/src/h5core/h5t_openclose.c
index 3289e68..d15a26b 100644
--- a/src/h5core/h5t_openclose.c
+++ b/src/h5core/h5t_openclose.c
@@ -67,8 +67,8 @@ _create_vertex_type (
 		h5priv_insert_hdf5_type (
 			f,
 			dtypes->h5_vertex_t,
-			"global_vid",
-			HOFFSET (struct h5_vertex, global_vid),
+			"global_idx",
+			HOFFSET (struct h5_vertex, global_idx),
 			H5_ID_T) );
 	TRY(
 		h5priv_insert_hdf5_type (
@@ -96,29 +96,29 @@ _create_triangle_type (
 		h5priv_insert_hdf5_type (
 			f,
 			dtypes->h5_triangle_t,
-			"global_eid",
-			HOFFSET (struct h5_triangle, global_eid),
+			"global_idx",
+			HOFFSET (struct h5_triangle, global_idx),
 			H5_ID_T) );
 	TRY(
 		h5priv_insert_hdf5_type (
 			f,
 			dtypes->h5_triangle_t,
-			"global_parent_eid",
-			HOFFSET (struct h5_triangle, global_parent_eid),
+			"global_parent_idx",
+			HOFFSET (struct h5_triangle, global_parent_idx),
 			H5_ID_T) );
 	TRY(
 		h5priv_insert_hdf5_type (
 			f,
 			dtypes->h5_triangle_t,
-			"global_child_eid",
-			HOFFSET(struct h5_triangle, global_child_eid),
+			"global_child_idx",
+			HOFFSET(struct h5_triangle, global_child_idx),
 			H5_ID_T) );
 	TRY(
 		h5priv_insert_hdf5_type (
 			f,
 			dtypes->h5_triangle_t,
-			"global_vids",
-			HOFFSET (struct h5_triangle, global_vids),
+			"global_vertex_indices",
+			HOFFSET (struct h5_triangle, global_vertex_indices),
 			dtypes->h5_3id_t) );
 
 	return H5_SUCCESS;
@@ -168,29 +168,29 @@ _create_tet_type (
 		h5priv_insert_hdf5_type (
 			f,
 			dtypes->h5_tet_t,
-			"global_eid",
-			HOFFSET (struct h5_tetrahedron, global_eid),
+			"global_idx",
+			HOFFSET (struct h5_tetrahedron, global_idx),
 			H5_ID_T) );
 	TRY(
 		h5priv_insert_hdf5_type (
 			f,
 			dtypes->h5_tet_t,
-			"global_parent_eid",
-			HOFFSET (struct h5_tetrahedron, global_parent_eid),
+			"global_parent_idx",
+			HOFFSET (struct h5_tetrahedron, global_parent_idx),
 			H5_ID_T) );
 	TRY(
 		h5priv_insert_hdf5_type (
 			f,
 			dtypes->h5_tet_t,
-			"global_child_eid",
-			HOFFSET (struct h5_tetrahedron, global_child_eid),
+			"global_child_idx",
+			HOFFSET (struct h5_tetrahedron, global_child_idx),
 			H5T_NATIVE_INT32) );
 	TRY(
 		h5priv_insert_hdf5_type (
 			f,
 			dtypes->h5_tet_t,
-			"global_vids",
-			HOFFSET (struct h5_tetrahedron, global_vids),
+			"global_vertex_indices",
+			HOFFSET (struct h5_tetrahedron, global_vertex_indices),
 			dtypes->h5_4id_t) );
 
 	return H5_SUCCESS;
diff --git a/src/h5core/h5t_readwrite.c b/src/h5core/h5t_readwrite.c
index a3ffde1..5bde170 100644
--- a/src/h5core/h5t_readwrite.c
+++ b/src/h5core/h5t_readwrite.c
@@ -255,20 +255,20 @@ build_elems_ldta (
 	     local_eid < num_elems;
 	     local_eid++, elp+=h5tpriv_sizeof_elem[t->mesh_type], el_data++) {
 		el = (h5_elem_t*)elp;
-		TRY( h5t_map_global_vids2local (
+		TRY( h5t_map_global_vertex_indices2local (
 			     f,
-			     el->global_vids,
+			     el->global_vertex_indices,
 			     num_vertices,
-			     el_data->local_vids) );
-		if (el->global_parent_eid >= 0)
-			TRY( el_data->local_parent_eid =
-			     h5t_map_global_eid2local (
-				     f, el->global_parent_eid) );
+			     el_data->local_vertex_indices) );
+		if (el->global_parent_idx >= 0)
+			TRY( el_data->local_parent_idx =
+			     h5t_map_global_elem_idx2local (
+				     f, el->global_parent_idx) );
 		
-		if (el->global_child_eid >= 0)
-			TRY( el_data->local_child_eid =
-			     h5t_map_global_eid2local (
-				     f, el->global_child_eid) );
+		if (el->global_child_idx >= 0)
+			TRY( el_data->local_child_idx =
+			     h5t_map_global_elem_idx2local (
+				     f, el->global_child_idx) );
 		
 		if (local_eid >= t->num_elems[level_id]) {
 			level_id++;
diff --git a/src/h5core/h5t_retrieve.c b/src/h5core/h5t_retrieve.c
index 3a94e71..d072253 100644
--- a/src/h5core/h5t_retrieve.c
+++ b/src/h5core/h5t_retrieve.c
@@ -36,8 +36,8 @@ h5tpriv_elem_is_on_cur_level (
 	) {
 	h5t_fdata_t* t = f->t;
 	if ( (el_dta->level_id > t->cur_level) ||
-	     ( (el_dta->local_child_eid >= 0) &&
-	       (el_dta->local_child_eid < t->num_elems[t->cur_level]) ) ) {
+	     ( (el_dta->local_child_idx >= 0) &&
+	       (el_dta->local_child_idx < t->num_elems[t->cur_level]) ) ) {
 		return H5_NOK;
 	}
 	return H5_SUCCESS;
diff --git a/src/h5core/h5t_store.c b/src/h5core/h5t_store.c
index e939797..d042e70 100644
--- a/src/h5core/h5t_store.c
+++ b/src/h5core/h5t_store.c
@@ -42,7 +42,7 @@ assign_global_vertex_indices (
 	for (local_idx = 0;
 	     local_idx < t->num_vertices[t->num_levels-1];
 	     local_idx++) {
-		t->vertices[local_idx].global_vid = local_idx;
+		t->vertices[local_idx].global_idx = local_idx;
 	}
 
 	return H5_SUCCESS;
@@ -77,13 +77,13 @@ assign_global_elem_indices (
 		default:
 			return h5_error_internal (f,__FILE__,__func__,__LINE__);
 		}
-		elem->global_eid = local_idx;
-		elem->global_parent_eid = elem_ldta->local_parent_eid;
-		elem->global_child_eid = elem_ldta->local_child_eid;
+		elem->global_idx = local_idx;
+		elem->global_parent_idx = elem_ldta->local_parent_idx;
+		elem->global_child_idx = elem_ldta->local_child_idx;
 		int i;
 		int num_vertices = t->ref_element->num_faces[0];
 		for (i = 0; i < num_vertices; i++) {
-			elem->global_vids[i] = elem_ldta->local_vids[i];
+			elem->global_vertex_indices[i] = elem_ldta->local_vertex_indices[i];
 		}
 	}
 
@@ -152,7 +152,7 @@ h5t_begin_store_vertices (
 h5_id_t
 h5t_store_vertex (
 	h5_file_t* const f,		/*!< file handle		*/
-	const h5_id_t global_vid,     	/*!< global vertex id or -1	*/
+	const h5_id_t global_idx,     	/*!< global vertex id or -1	*/
 	const h5_float64_t P[3]		/*!< coordinates		*/
 	) {
 	h5t_fdata_t* const t = f->t;
@@ -170,11 +170,11 @@ h5t_store_vertex (
 	if (t->cur_level < 0)
 		return h5tpriv_error_undef_level(f);
 
-	h5_id_t local_id = ++t->last_stored_vid;
-	h5_vertex_t *vertex = &t->vertices[local_id];
-	vertex->global_vid = global_vid;     /* ID from mesher, replaced later!*/
+	h5_id_t local_idx = ++t->last_stored_vid;
+	h5_vertex_t *vertex = &t->vertices[local_idx];
+	vertex->global_idx = global_idx;     /* ID from mesher, replaced later!*/
 	memcpy (&vertex->P, P, sizeof (vertex->P));
-	return local_id;
+	return local_idx;
 }
 
 h5_err_t
@@ -261,13 +261,14 @@ h5t_store_elem (
 	h5_id_t elem_idx = ++t->last_stored_eid;
 	h5_elem_ldta_t* elem_ldta = &t->elems_ldta[elem_idx];
 
-	elem_ldta->local_parent_eid = elem_idx_of_parent;
-	elem_ldta->local_child_eid = -1;
+	elem_ldta->local_parent_idx = elem_idx_of_parent;
+	elem_ldta->local_child_idx = -1;
 	elem_ldta->level_id = t->cur_level;
 	int num_vertices = t->ref_element->num_faces[0];
-	memcpy (elem_ldta->local_vids, vertices,
+	memcpy (elem_ldta->local_vertex_indices, vertices,
 		 sizeof (*vertices) * num_vertices);
-	h5tpriv_sort_local_vids (f, elem_ldta->local_vids, num_vertices);
+	h5tpriv_sort_local_vertex_indices (f, elem_ldta->local_vertex_indices,
+					   num_vertices);
 	h5_id_t face_idx;
 	int num_faces = t->ref_element->num_faces[1];
 	h5_idlist_t* retval;
diff --git a/src/h5core/h5t_store_tetm.c b/src/h5core/h5t_store_tetm.c
index 61c7e16..40c5bfb 100644
--- a/src/h5core/h5t_store_tetm.c
+++ b/src/h5core/h5t_store_tetm.c
@@ -46,7 +46,7 @@ alloc_tets (
 	h5_id_t *p = t->elems_lvids;
 	h5_id_t id;
 	for ( id = 0; id < new; id++, p+=nvertices ) {
-		t->elems_ldta[id].local_vids = p;
+		t->elems_ldta[id].local_vertex_indices = p;
 	}
 
 	/* alloc mem for global to local ID mapping */
@@ -110,7 +110,7 @@ bisect_edge (
 	for ( i = 0; i < retval->num_items; i++ ) {
 		h5_id_t local_id = h5tpriv_get_elem_idx ( retval->items[i] );
 		h5_elem_ldta_t *tet = &t->elems_ldta[local_id];
-		if ( tet->local_child_eid >= 0 ) {
+		if ( tet->local_child_idx >= 0 ) {
 			/*
 			  this element has been refined!
 			  return bisecting point
@@ -121,7 +121,7 @@ bisect_edge (
 			TRY( get_direct_children_of_edge (
 				     f,
 				     face_id,
-				     tet->local_child_eid,
+				     tet->local_child_idx,
 				     kids) );
 			TRY( h5t_get_vertex_indices_of_edge (f, kids[0], edge0) );
 			TRY( h5t_get_vertex_indices_of_edge (f, kids[1], edge1) );
@@ -160,16 +160,16 @@ refine_tet (
 	h5_id_t elem_idx_of_first_child;
 	h5_elem_ldta_t *tet = &t->elems_ldta[elem_idx];
 
-	if ( tet->local_child_eid >= 0 )
+	if ( tet->local_child_idx >= 0 )
 		return h5_error (
 			f,
 			H5_ERR_INVAL,
 			"Tetrahedron %lld already refined.",
 			elem_idx );
-	vertices[0] = tet->local_vids[0];
-	vertices[1] = tet->local_vids[1];
-	vertices[2] = tet->local_vids[2];
-	vertices[3] = tet->local_vids[3];
+	vertices[0] = tet->local_vertex_indices[0];
+	vertices[1] = tet->local_vertex_indices[1];
+	vertices[2] = tet->local_vertex_indices[2];
+	vertices[3] = tet->local_vertex_indices[3];
 
 	vertices[4] = bisect_edge (f, 0, elem_idx);
 	vertices[5] = bisect_edge (f, 1, elem_idx);
@@ -231,8 +231,8 @@ refine_tet (
 	new_elem[3] = vertices[9];
 	TRY( h5t_store_elem (f, elem_idx, new_elem) );
 
-	t->elems.tets[elem_idx].global_child_eid = elem_idx_of_first_child;
-	t->elems_ldta[elem_idx].local_child_eid = elem_idx_of_first_child;
+	t->elems.tets[elem_idx].global_child_idx = elem_idx_of_first_child;
+	t->elems_ldta[elem_idx].local_child_idx = elem_idx_of_first_child;
 	t->num_elems_on_level[t->cur_level]--;
 
 	return elem_idx_of_first_child;
diff --git a/src/h5core/h5t_store_trim.c b/src/h5core/h5t_store_trim.c
index baef76d..5e6d0d0 100644
--- a/src/h5core/h5t_store_trim.c
+++ b/src/h5core/h5t_store_trim.c
@@ -46,7 +46,7 @@ alloc_triangles (
 	h5_id_t *p = t->elems_lvids;
 	h5_id_t id;
 	for ( id = 0; id < new; id++, p+=nvertices ) {
-		t->elems_ldta[id].local_vids = p;
+		t->elems_ldta[id].local_vertex_indices = p;
 	}
 
 	/* alloc mem for global to local ID mapping */
@@ -106,7 +106,7 @@ bisect_edge (
 	for ( i = 0; i < retval->num_items; i++ ) {
 		h5_id_t local_id = h5tpriv_get_elem_idx ( retval->items[i] );
 		h5_elem_ldta_t *tet = &t->elems_ldta[local_id];
-		if ( tet->local_child_eid >= 0 ) {
+		if ( tet->local_child_idx >= 0 ) {
 			/*
 			  this element has been refined!
 			  return bisecting point
@@ -117,7 +117,7 @@ bisect_edge (
 			TRY ( get_direct_children_of_edge (
 				      f,
 				      face_id,
-				      tet->local_child_eid,
+				      tet->local_child_idx,
 				      kids ) );
 			TRY ( h5t_get_vertex_indices_of_edge ( f, kids[0], edge0 ) );
 			TRY ( h5t_get_vertex_indices_of_edge ( f, kids[1], edge1 ) );
@@ -158,16 +158,16 @@ refine_triangle (
 	h5_id_t elem_idx_of_first_child;
 	h5_elem_ldta_t *el = &t->elems_ldta[elem_idx];
 
-	if ( el->local_child_eid >= 0 )
+	if ( el->local_child_idx >= 0 )
 		return h5_error (
 			f,
 			H5_ERR_INVAL,
 			"Element %lld already refined.",
 			elem_idx );
 
-	vertices[0] = el->local_vids[0];
-	vertices[1] = el->local_vids[1];
-	vertices[2] = el->local_vids[2];
+	vertices[0] = el->local_vertex_indices[0];
+	vertices[1] = el->local_vertex_indices[1];
+	vertices[2] = el->local_vertex_indices[2];
 
 	vertices[3] = bisect_edge( f, 0, elem_idx );
 	vertices[4] = bisect_edge( f, 1, elem_idx );
@@ -195,8 +195,8 @@ refine_triangle (
 	new_elem[2] = vertices[5];
 	TRY( h5t_store_elem (f, elem_idx, new_elem) );
 
-	t->elems.tris[elem_idx].global_child_eid = elem_idx_of_first_child;
-	t->elems_ldta[elem_idx].local_child_eid = elem_idx_of_first_child;
+	t->elems.tris[elem_idx].global_child_idx = elem_idx_of_first_child;
+	t->elems_ldta[elem_idx].local_child_idx = elem_idx_of_first_child;
 	t->num_elems_on_level[t->cur_level]--;
 
 	return elem_idx_of_first_child;
diff --git a/src/h5core/h5t_types_private.h b/src/h5core/h5t_types_private.h
index 84cca6f..aed208d 100644
--- a/src/h5core/h5t_types_private.h
+++ b/src/h5core/h5t_types_private.h
@@ -47,7 +47,7 @@ struct h5t_methods {
 };
 
 typedef struct h5_vertex {
-	h5_id_t		global_vid;
+	h5_id_t		global_idx;
 	h5_coord3d_t	P;
 } h5_vertex_t;
 
@@ -56,32 +56,32 @@ typedef struct h5_vertex_data {
 } h5_vertex_data_t;
 
 typedef struct h5_triangle {
-	h5_id_t		global_eid;
-	h5_id_t		global_parent_eid;
-	h5_id_t		global_child_eid;
-	h5_3id_t	global_vids;
+	h5_id_t		global_idx;
+	h5_id_t		global_parent_idx;
+	h5_id_t		global_child_idx;
+	h5_3id_t	global_vertex_indices;
 } h5_triangle_t;
 
 typedef struct h5_tetrahedron {
-	h5_id_t		global_eid;
-	h5_id_t		global_parent_eid;
-	h5_id_t		global_child_eid;
-	h5_4id_t	global_vids;
+	h5_id_t		global_idx;
+	h5_id_t		global_parent_idx;
+	h5_id_t		global_child_idx;
+	h5_4id_t	global_vertex_indices;
 } h5_tetrahedron_t;
 typedef h5_tetrahedron_t	h5_tet_t;
 
 typedef struct h5_elem {
-	h5_id_t		global_eid;
-	h5_id_t		global_parent_eid;
-	h5_id_t		global_child_eid;
-	h5_id_t		global_vids[1];
+	h5_id_t		global_idx;
+	h5_id_t		global_parent_idx;
+	h5_id_t		global_child_idx;
+	h5_id_t		global_vertex_indices[1];
 } h5_elem_t;
 
 typedef struct h5_elem_ldta {
-	h5_id_t		local_parent_eid;
-	h5_id_t		local_child_eid;
+	h5_id_t		local_parent_idx;
+	h5_id_t		local_child_idx;
 	h5_id_t		level_id;
-	h5_id_t		*local_vids;
+	h5_id_t		*local_vertex_indices;
 } h5_elem_ldta_t;
 
 
diff --git a/src/include/h5core/h5t_map.h b/src/include/h5core/h5t_map.h
index 8e70109..0c3049a 100644
--- a/src/include/h5core/h5t_map.h
+++ b/src/include/h5core/h5t_map.h
@@ -2,17 +2,17 @@
 #define __H5T_MAP_H
 
 h5_id_t
-h5t_map_global_vid2local (
+h5t_map_global_vertex_index2local (
 	h5_file_t * const f,
-	h5_id_t global_vid
+	h5_id_t global_idx
 	);
 
 h5_err_t
-h5t_map_global_vids2local (
+h5t_map_global_vertex_indices2local (
 	h5_file_t *f,
-	const h5_id_t * const global_vids,
+	const h5_id_t * const global_indices,
 	const h5_id_t size,
-	h5_id_t * const local_vids
+	h5_id_t * const local_indices
 	);
 
 h5_id_t
@@ -22,9 +22,9 @@ h5t_map_local_vid2global (
 	);
 
 h5_id_t
-h5t_map_global_eid2local (
+h5t_map_global_elem_idx2local (
 	h5_file_t * const f,
-	const h5_id_t global_eid
+	const h5_id_t global_idx
 	);
 
 h5_id_t